3 


PHYSICSJ3EPT 


HM 


VISUAL    ILLUSIONS 

THEIR  CAUSES,  CHARACTERISTICS 
AND  APPLICATIONS 


BY 

M.  LTJCKIESH 

DIRECTOR  OF  APPLIED  SCIENCE,  NELA  RESEARCH  LABORATORIES, 
NATIONAL  LAMP  WORKS  OF  GENERAL  ELECTRIC  CO. 

AUTHOR  OF  "COLOR  AND  ITS  APPLICATIONS,"  "LIGHT  AND  SHADE 
AND  THEIR  APPLICATIONS,"  "  THE  LIGHTING  ART,"  THE 
LANGUAGE  OF  COLOR,"  "ARTIFICIAL  LIGHT— ITS 
INFLUENCE  UPON  CIVILIZATION," 
"LIGHTING  THE  HOME,"  ETC. 


100  ILLUSTRATIONS 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

EIGHT  WARREN  STREET 

1922 


PHYSICS 


COPYRIGHT,  1922,  BY 
D.  VAN  NOSTRAND  COMPANY 


PREFACE 

EVENTUALLY  one  of  the  results  of  application  to 
the  analysis  and  measurement  of  the  phenomena 
of  light,  color,  lighting,  and  vision  is  a  firmly 
entrenched  conviction  of  the  inadequacy  of  physical 
measurements  as  a  means  for  representing  what  is 
perceived.  Physical  measurements  have  supplied 
much  of  the  foundation  of  knowledge  and  it  is  not  a 
reflection  upon  their  great  usefulness  to  state  that 
often  they  differ  from  the  results  of  intellectual  ap- 
praisal through  the  visual  sense.  In  other  words,  there 
are  numberless  so-called  visual  illusions  which  must 
be  taken  into  account.  All  are  of  interest;  many  can 
be  utilized;  and  some  must  be  suppressed. 

Scientific  literature  yields  a  great  many  valuable 
discussions  from  theoretical  and  experimental  view- 
points but  much  of  the  material  is  controversial.  The 
practical  aspects  of  visual  illusions  have  been  quite 
generally  passed  by  and,  inasmuch  as  there  does  not 
appear  to  be  a  volume  available  which  treats  the  sub- 
ject in  a  condensed  manner  but  with  a  broad  scope, 
this  small  volume  is  contributed  toward  filling  the 
gap. 

The  extreme  complexity  of  the  subject  is  recognized, 
but  an  attempt  toward  simplicity  of  treatment  has  been 
made  by  confining  the  discussion  chiefly  to'  static 
visual  illusions,  by  suppressing  minor  details,  and  by 


iv  PREFACE 


subordinating  theory.  In  other  words,  the  intent  has 
been  to  emphasize  experimental  facts.  Even  these 
are  so  numerous  that  only  the  merest  glimpses  of 
various  aspects  can  be  given  in  order  to  limit  the  text 
to  a  small  volume.  Some  theoretical  aspects  of  the 
subject  are  still  extremely  controversial,  so  they  are 
introduced  only  occasionally  and  then  chiefly  for  the 
purpose  of  illustrating  the  complexities  and  the  trends 
of  attempted  explanations.  Space  does  not  even  ad- 
mit many  qualifications  which  may  be  necessary  in 
order  to  escape  criticism  entirely. 

The  visual  illusions  discussed  are  chiefly  of  the 
static  type,  although  a  few  others  have  been  intro- 
duced. Some  of  the  latter  border  upon  motion, 
others  upon  hallucinations,  and  still  others  produced 
by  external  optical  media  are  illusions  only  by  exten- 
sion of  the  term.  These  exceptions  are  included  for 
the  purpose  of  providing  glimpses  into  the  border- 
lands. 

It  is  hoped  that  this  condensed  discussion,  which 
is  ambitious  only  in  scope,  will  be  of  interest  to  the 
general  reader,  to  painters,  decorators,  and  architects, 
to  lighting  experts,  and  to  all  interested  in  light,  color, 
and  vision.  It  is  an  essential  supplement  to  certain 
previous  works. 

November,  1920.  M.  LUCKIESH 


CONTENTS 

CHAPTER  PAGE 

I.  Introduction 1 

II.  The  eye 13 

III.  Vision 29 

IV.  Some  types  of  geometrical  illusions 44 

V.  Equivocal  figures : 64 

VI.  The  influence  of  angles 76 

VII.  Illusions  of  depth  and  of  distance 102 

VIII.  Irradiation  and  brightness-contrast 114 

IX.  Color 124 

X.  Lighting 144 

XI.  Nature 164 

XII.  Painting  and  decoration 179 

XIII.  Architecture 195 

XIV.  Mirror  Magic 205 

XV.  Camouflage 210 


LIST  OF  ILLUSTRATIONS 

FIGURE  PAGE 

1.  Principal  parts  of  the  eye 14 

2.  Stereoscopic  pictures  for  combining  by  converging  or  diverging  the 

optical  axes 41 

3.  Stereoscopic  pictures 41 

4.  The  vertical  line  appears  longer  than  the  equal  horizontal  line  in 

each  case 46 

5.  The  vertical  dimension  is  equal  to  the  horizontal  one,  but  the 

former  appears  greater 47 

6.  The  divided  or  filled  space  on  the  left  appears  longer  than  the  equal 

space  on  the  right ; 49 

7.  The  three  lines  are  of  equal  length 50 

8.  The  distance  between  the  two  circles  on  the  left  is  equal  to  the 

distance  between  the  outside  edges  of  the  two  circles  on  the 

right.  . . 60 

9.  Three  squares  of  equal  dimensions  which  appear  different  in  area 

and  dimension 61 

10.  The  vertical  distance  between  the  upper  circle  and  the  left-hand 

one  of  the  group  is  equal  to  the  overall  length  of  the  group  of 

three  circles 62 

11.  Two  equal  semi-circles .  .  . 63 

12.  Arcs  of  the  same  circle 63 

13.  Three  incomplete  but  equal  squares 53 

14.  Middle  sections  of  the  two  lines  are  equal 64 

15.  An  effect  of  contrasting  areas  (Baldwin's  figure) 54 

16.  An  illusion  of  contrast 56 

17.  Equal  circles  which  appear  unequal  due  to  contrast  (Ebbinghaus' 

figure) 56 

18.  Equal  circles  appearing  unequal  owing  to  contrasting  concentric 

circles 56 

19.  Circles  influenced  by  position  within  an  angle 67 

20.  Contrasting  angles 57 

21.  Owing  to  perspective  the  right  angles  appear  oblique  and  vice 

versa 58 

22.  Two  equal  diagonals  which  appear  unequal 68 

23.  Apparent  variations  in  the  distance  between  two  parallel  lines ....  69 

24.  A  striking  illusion  of  perspective 60 

25.  Distortion  of  a  square  due  to  superposed  lines 61 

26.  Distortion  of  a  circle  due  to  superposed  lines 62 

27.  Illustrating  fluctuation  of  attention 65 

28.  The  grouping  of  the  circles  fluctuates 66 

29.  Crossed  lines  which  may  be  interpreted  in  two  ways 67 

vii 


viii  LIST  OF  ILLUSTRATIONS 

30.  Reversible  cubes 68 

31.  The  reversible  "  open  book  "  (after  Mach) 69 

32.  A  reversible  tetrahedron 69 

33.  Reversible  perspective  of  a  group  of  rings  or  of  a  tube 70 

34.  Schroder's  reversible  staircase 70 

35.  Thiery's  figure 71 

36.  Illustrating  certain  influences  upon  the  apparent  direction  of  vision. 

By  covering  all  but  the  eyes  the  latter  appear  to  be  drawn  alike 

in  both  sketches 73 

37.  Zollner's  illusion  of  direction 77 

38.  Parallel  lines  which  do  not  appear  so 79 

39.  Wundt's  illusion  of  direction 79 

40.  Bering's  illusion  of  direction 80 

41.  Simple  effect  of  angles 81 

42.  The  effect  of  two  angles  in  tilting  the  horizontal  lines 83 

43.  The  effect  of  crossed  lines  upon  then-  respective  apparent  di- 

rections    83 

44.  Another  step  toward  the  Zollner  illusion 84 

45.  The  two  diagonals  would  meet  on  the  left  vertical  line 85 

46.  Poggendorff's  illusion.    Which  oblique  line  on  the  right  is  the  pro- 

longation of  the  oblique  line  on  the  left? 85 

47.  A  straight  line  appears  to  sag 86 

48.  Distortions  of  contour  due  to  contact  with  other  contours 87 

49.  An  illusion  of  direction 88 

60.  "  Twisted-cord  "  illusion.    These  are  straight  cords 89 

61.  "  Twisted-cord  "  illusion.    These  are  concentric  circles 89 

52.   A  spiral  when  rotated  appears  to  expand  or  contract,  depending 

upon  direction  of  rotation 90 

63.  Angles  affect  the  apparent  length  of  lines 91 

64.  The  horizontal  line  appears  to  tilt  downward  toward  the  ends ....  92 

65.  The  horizontal  line  appears  to  sag  in  the  middle 92 

66.  The  Miiller-Lyer  illusion 93 

57.   Combined  influence  of  angles  and  contrasting  lengths 95 

68.  Two  equal  oblique  lines  appear  unequal  because  of  then*  different 

positions . 95 

59.  An  illusion  of  area 96 

60.  Five  equal  areas  showing  the  influence  of  contour  upon  judgment 

of  area 97 

61.  Showing  the  effect  of  directing  the  attention 98 

62.  Simple  apparatus  for  demonstrating  the  remarkable   effects  of 

contrasts  in  brightness  and  color 115 

63.  Illustrating  brightness-contrast 117 

64.  An  effect  of  brightness-contrast.    Note  the  darkening  of  the  niter- 

sections  of  the  white  strips 118 

66.  The  phenomenon  of  irradiation 121 

66.  An  excellent  pattern  for  demonstrating  color-contrast 126 

67.  By  rotating  this  Mason  (black  and  white)  disk  color-sensations 

are  produced 133 


LIST  OF  ILLUSTRATIONS  ix 

68.  For  demonstrating  retiring  and  advancing  colors 137 

69.  By  combining  these  stereoscopically  the  effect  of  metallic  lustre 

(similar  to  graphite  in  this  case)  is  obtained 141 

70.  A  bas-relief  lighted  from  above 146 

71.  An  intaglio  lighted  from  above 147 

72.  A  bas-relief  lighted  from  the  left 148 

73.  An  intaglio  lighted  from  the  left 149 

74a.  A  disk  (above)  and  a  sphere  (below)  lighted  from  overhead. . . .  145 

b.  A  disk  and  a  sphere  lighted  by  perfectly  diffused  light 145 

75.  A  concave  hemispherical  cup  on  the  left  and  a  convex  hemisphere 

on  the  right  lighted  by  a  light-source  of  large  angle  such  as  a 
window 150 

76.  The  same  as  Fig.  75,  but  lighted  by  a  very  small  light-source 151 

77.  Apparent  ending  of  a  searchlight  beam 161 

78.  An  accurate  tracing  from  a  photograph  (continual  exposure)  of  the 

moon  rising 171 

79.  Accurate  tracings  from  a  photograph  (short  exposures  at  intervals) 

of  the  sun  setting 172 

80.  Explanation  offered  by   Smith  of  the  apparent   enlargement  of 

heavenly  bodies  near  the  horizon 174 

81.  Explanation  of  a  common  mirage 176 

82.  Illustrating  the  apparent  distortion  of  a  picture  frame  in  which 

the  grain  of  the  wood  is  visible 190 

83.  Another  example  similar  to  Fig.  82 191 

84.  From  actual  photographs  of  the  end-grain  of  a  board 192 

85.  Exaggerated  illusions  in  architecture 198 

86.  Illustrating  the  influence  of  visual  angle  upon  apparent  vertical 

height 199 

87.  Irradiation  in  architecture 200 

88.  Some  simple  geometrical-optical  illusions  in  architecture 201 

89.  By  decreasing  the  exposed  length  of  shingles  toward  the  top  a 

greater  apparent  expanse  is  obtained 202 

90.  An  example  of  a  mirror  "  illusion  " 207 

91.  Another  example  of  "  mirror  magic  " 208 

92.  A  primary  stage  in  the  evolution  of  the  use  of  geometrical-optical 

illusions  on  ships 226 

93  and  94.  Attempts  at  distortion  of  outline  which  preceded  the 

adoption  of  geometrical-optical  illusions 228 

95  and  96.  Illustrating  the  use  of  models  by  the  Navy  Department  in 

developing  the  geometrical-optical  illusion  for  ships 229 

97  and  98.  Examples  of  the  geometrical-optical  illusion  as  finally 

applied 231 

99.  Representative  earth  backgrounds  for  an  airplane  (uncamouflaged) 

as  viewed  from  above 235 

100.  Illustrating  the  study  of  pattern  for  airplanes.     The  photograph 

was  taken  from  an  altitude  of  10,000  feet.  The  insert  shows 
the  relative  lengths  (vertical  scale)  of  an  airplane  of  50-foot 
spread  at  various  distances  below  the  observer 239 


VISUAL  ILLUSIONS 

i 

INTRODUCTION 

SEEING  is  deceiving.  Thus  a  familiar  epigram 
may  be  challenged  in  order  to  indicate  the 
trend  of  this  book  which  aims  to  treat  certain 
phases  of  visual  illusions.  In  general,  we  do  not  see 
things  as  they  are  or  as  they  are  related  to  each  other; 
that  is,  the  intellect  does  not  correctly  interpret  the 
deliverances  of  the  visual  sense,  although  sometimes 
the  optical  mechanism  of  the  eyes  is  directly  respon- 
sible for  the  illusion.  In  other  words,  none  of  our 
conceptions  and  perceptions  are  quite  adequate,  but 
fortunately  most  of  them  are  satisfactory  for  practical 
purposes.  Only  a  part  of  what  is  perceived  comes 
through  the  senses  from  the  object;  the  remainder 
always  comes  from  within.  In  fact,  it  is  the  visual 
sense  or  the  intellect  which  is  responsible  for  illusions 
of  the  various  types  to  be  discussed  in  the  follow- 
ing chapters.  Our  past  experiences,  associations, 
desires,  demands,  imaginings,  and  other  more  or  less 
obscure  influences  create  illusions. 

An  illusion  does  not  generally  exist  physically  but 
it  is  difficult  in  some  cases  to  explain  the  cause.  Cer- 
tainly there  are  many  cases  of  errors  of  judgment. 

A  mistaken  estimate  of  the  distance  of  a  mountain 

i 


2 : :' :  —  :  - :    '*'•«:  /'VISUAL  ILLUSIONS 

is  due  to  an  error  of  judgment  but  the  perception  of 
a  piece  of  white  paper  as  pink  on  a  green  background 
is  an  error  of  sense.  It  is  realized  that  the  foregoing 
comparison  leads  directly  to  one  of  the  most  contro- 
versial questions  in  psychology,  but  there  is  no  in- 
tention on  the  author's  part  to  cling  dogmatically  to 
the  opinions  expressed.  In  fact,  discussions  of  the 
psychological  judgment  involved  in  the  presentations 
of  the  visual  sense  are  not  introduced  with  the  hope 
of  stating  the  final  word  but  to  give  the  reader  an  idea 
of  the  inner  process  of  perception.  The  final  word 
will  be  left  to  the  psychologists  but  it  appears  possible 
that  it  may  never  be  formulated. 

In  general,  a  tree  appears  of  greater  length  when 
standing  than  when  lying  upon  the  ground.  Lines, 
areas,  and  masses  are  not  perceived  in  their  actual 
physical  relations.  The  appearance  of  a  colored  ob- 
ject varies  considerably  with  its  environment.  The 
sky  is  not  perceived  as  infinite  space  nor  as  a  hemi- 
spherical dome,  but  as  a  flattened  vault.  The  moon 
apparently  diminishes  in  size  as  it  rises  toward  the 
zenith.  A  bright  object  appears  larger  than  a  dark 
object  of  the  same  physical  dimensions.  Flat  areas 
may  appear  to  have  a  third  dimension  of  depth.  And 
so  on. 

Illusions  are  so  numerous  and  varied  that  they 
have  long  challenged  the  interest  of  the  scientist. 
They  may  be  so  useful  or  even  so  disastrous  that 
they  have  been  utilized  or  counteracted  by  the  skilled 
artist  or  artisan.  The  architect  and  painter  have 
used  or  avoided  them.  The  stage-artist  employs 
them  to  carry  the  audience  in  its  imagination  to  other 


INTRODUCTION 


environments  or  to  far  countries.  The  magician  has 
employed  them  in  his  entertainments  and  the  camou- 
fleur  used  them  to  advantage  in  the  practice  of  de- 
ception during  the  recent  war.  They  are  vastly  en- 
tertaining, useful,  deceiving,  or  disastrous,  depending 
upon  the  viewpoint. 

Incidentally,  a  few  so-called  illusions  will  be  dis- 
cussed which  are  not  due  strictly  to  errors  of  the 
visual  sense  or  of  the  intellect.  Examples  of  these 
are  the  mirage  and  certain  optical  effects  employed 
by  the  magician.  In  such  cases  neither  the  visual 
sense  nor  the  intellect  errs.  In  the  case  of  the  mirage 
rays  of  light  coming  from  the  object  to  the  eye  are 
bent  from  their  usual  straight-line  course  and  the 
object  appears  to  be  where  it  really  is  not.  However, 
with  these  few  exceptions,  which  are  introduced  for 
their  specific  interest  and  for  the  emphasis  they  give 
to  the  "true"  illusion,  it  will  be  understood  that 
illusions  in  general  as  hereinafter  discussed  will  mean 
those  due  to  the  visual  mechanism  or  to  errors  of 
judgment  or  intellect.  For  the  sake  of  brevity  we 
might  say  that  they  are  those  due  to  errors  of  visual 
perception.  Furthermore,  only  those  of  a  "static" 
type  will  be  considered;  that  is,  the  vast  complexi- 
ties due  to  motion  are  not  of  interest  from  the  view- 
point of  the  aims  of  this  book. 

There  are  two  well-known  types  of  misleading  per- 
ceptions, namely  illusions  and  hallucinations.  If,  for 
example,  two  lines  appear  of  equal  length  and  are  not, 
the  error  in  judgment  is  responsible  for  what  is  termed 
an  "  illusion."  If  the  perceptual  consciousness  of  an 
object  appears  although  the  object  is  not  present,  the 


4  VISUAL  ILLUSIONS 


result  is  termed  an  "  hallucination."  For  example,  if 
something  is  seen  which  does  not  exist,  the  essential 
factors  are  supplied  by  the  imagination.  Shadows  are 
often  wrought  by  the  imagination  into  animals  and 
even  human  beings  bent  upon  evil  purpose.  Ghosts 
are  created  in  this  manner.  Hallucinations  depend 
largely  upon  the  recency,  frequency,  and  vividness  of 
past  experience.  A  consideration  of  this  type  of  mis- 
leading perception  does  not  advance  the  aims  of  this 
book  and  therefore  will  be  omitted. 

The  connection  between  the  material  and  mental 
in  vision  is  incomprehensible  and  apparently  must 
ever  remain  so.  Objects  emit  or  reflect  light  and  the 
optical  mechanism  known  as  the  eye  focuses  images 
of  the  objects  upon  the  retina.  Messages  are  then 
carried  to  the  brain  where  certain  molecular  vibra- 
tions take  place.  The  physiologist  records  certain 
physical  and  chemical  effects  in  the  muscles,  nerves, 
and  brain  and  behold!  there  appears  consciousness, 
sensations,  thoughts,  desires,  and  volitions.  How? 
and,  Why?  are  questions  which  may  never  be 
answered. 

It  is  dangerous  to  use  the  word  never,  but  the  ulti- 
mate answers  to  those  questions  appear  to  be  so  re- 
mote that  it  discourages  one  from  proceeding  far 
over  the  hazy  course  which  leads  toward  them.  In 
fact,  it  does  not  appreciably  further  the  aims  of  this 
book  to  devote  much  space  to  efforts  toward  explana- 
tion. In  covering  this  vast  and  complex  field  there 
are  multitudes  of  facts,  many  hypotheses,  and  numer- 
ous theories  from  which  to  choose.  Judgment  dic- 
tates that  of  the  limited  space  most  of  it  be  given  to 


INTRODUCTION 


the  presentation  of  representative  facts.  This  is  the 
reasoning  which  led  to  the  formulation  of  the  outline 
of  chapters. 

Owing  to  the  vast  complex  beyond  the  physical 
phenomena,  physical  measurements  upon  objects  and 
space  which  have  done  so  much  toward  building  a 
solid  foundation  for  scientific  knowledge  fail  ulti- 
mately to  provide  an  exact  mathematical  picture  of 
that  which  is  perceived.  Much  of  the  author's  previous 
work  has  been  devoted  to  the  physical  realities  but 
the  ever-present  differences  between  physical  and  per- 
ceptive realities  have  emphasized  the  need  for  con- 
sidering the  latter  as  well. 

Illusions  are  legion.  They  greet  the  careful  ob- 
server on  every  hand.  They  play  a  prominent  part 
in  our  appreciation  of  the  physical  world.  Sometimes 
they  must  be  avoided,  but  often  they  may  be  put  to 
work  in  various  arts.  Their  widespread  existence  and 
their  forcefulness  make  visual  perception  the  final 
judge  in  decoration,  in  painting,  in  architecture,  in 
landscaping,  in  lighting,  and  in  other  activities.  The 
ultimate  limitation  of  measurements  with  physical 
instruments  leaves  this  responsibility  to  the  intel- 
lect. The  mental  being  is  impressed  with  things  as 
perceived,  not  with  things  as  they  are.  It  is  believed 
that  this  intellectual  or  judiciary  phase  which  plays 
such  a  part  in  visual  perception  will  be  best  brought 
out  by  examples  of  various  types  of  static  illusions 
coupled  with  certain  facts  pertaining  to  the  eye  and 
to  the  visual  process  as  a  whole. 

In  special  simple  cases  it  is  not  difficult  to  deter- 
mine when  or  how  nearly  a  perception  is  true  but  in 


6  VISUAL  ILLUSIONS 

general,  agreement  among  normal  persons  is  neces- 
sary owing  to  the  absence  of  any  definite  measuring 
device  which  will  span  the  gap  between  the  percep- 
tion and  the  objective  reality.  Illusions  are  some- 
times called  "  errors  of  sense  "  and  some  of  them  are 
such,  but  often  they  are  errors  of  the  intellect.  The 
senses  may  deliver  correctly  but  error  may  arise  from 
imagination,  inexperience,  false  assumptions,  and  in- 
correct associations,  and  the  recency,  frequency,  and 
vividness  of  past  experience.  The  gifts  of  sight  are 
augmented  by  the  mind  with  judgments  based  upon 
experience  with  these  gifts. 

The  direct  data  delivered  by  the  visual  sense  are 
light,  intensity,  color,  direction.  These  may  be  con- 
sidered as  simple  or  elemental  sensations  because 
they  cannot  be  further  simplified  or  analyzed.  At 
this  point  it  is  hoped  that  no  controversy  with  the 
psychologist  will  be  provoked.  In  the  space  available 
it  appears  unfruitful  to  introduce  the  many  qualifica- 
tions necessary  to  satisfy  the,  as  yet  uncertain  or  at 
least  conflicting,  definitions  and  theories  underlying 
the  science  of  psychology.  If  it  is  necessary  to  add 
darkness  to  the  foregoing  group  of  elemental  visual 
sensations,  this  will  gladly  be  agreed  to. 

The  perceptions  of  outline-form  and  surface-con- 
tents perhaps  rank  next  in  simplicity;  however,  they 
may  be  analyzed  into  directions.  The  perception  of 
these  is  so  direct  and  so  certain  that  it  may  be  consid- 
ered to  be  immediate.  A  ring  of  points  is  apparently 
very  simple  and  it  might  be  considered  a  direct  sense- 
perception,  but  it  consists  of  a  number  of  elemental 
directions. 


INTRODUCTION 


The  perception  of  solid-form  is  far  more  complex 
than  outline-form  and  therefore  more  liable  to  error. 
It  is  judged  partially  by  binocular  vision  or  perspec- 
tive and  partly  by  the  distribution  of  light  and  shade. 
Colors  may  help  to  mold  form  and  even  to  give  depth 
to  flat  surfaces.  For  example,  it  is  well  known  that 
some  colors  are  "  advancing "  and  others  are 
"  retiring." 

Perhaps  of  still  greater  complexity  are  the  judg- 
ments of  size  and  of  distance.  Many  comparisons 
enter  such  judgments.  The  unconscious  acts  of  the 
muscles  of  the  eye  and  various  external  conditions 
such  as  the  clearness  of  the  atmosphere  play  promi- 
nent parts  in  influencing  judgment.  Upon  these  are 
superposed  the  numerous  psycho-physiological  phe- 
nomena of  color,  irradiation,  etc. 

In  vision  judgments  are  quickly  made  and  the 
process  apparently  is  largely  outside  of  consciousness. 
Higher  and  more  complex  visual  judgments  pass  into 
still  higher  and  more  complex  intellectual  judgments. 
All  these  may  appear  to  be  primary,  immediate,  in- 
nate, or  instinctive  and  therefore,  certain,  but  the 
fruits  of  studies  of  the  psychology  of  vision  have  shown 
that  these  visual  judgments  may  be  analyzed  into 
simpler  elements.  Therefore,  they  are  liable  to  error. 

That  the  ancients  sensed  the  existence  or  possi- 
bility of  illusions  is  evidenced  by  the  fact  that  they 
tried  to  draw  and  to  paint  although  their  inability  to 
observe  carefully  is  indicated  by  the  absence  of  true 
shading.  The  architecture  of  ancient  Greece  reveals 
a  knowledge  of  certain  illusions  in  the  efforts  to  over- 
come them.  However,  the  study  of  illusions  did  not 


8  VISUAL  ILLUSIONS 

engage  the  attention  of  scientists  until  a  compara- 
tively recent  period.  Notwithstanding  this  belated 
attention  there  is  a  vast  scientific  literature  pertaining 
to  the  multitudinous  phases  of  the  subject;  however, 
most  of  it  is  fragmentary  and  much  of  it  is  controversial. 
Some  of  it  deals  with  theory  for  a  particular  and  often 
a  very  simple  case.  In  life  complex  illusions  are  met 
but  at  present  it  would  be  futile  to  attempt  to  explain 
them  in  detail.  Furthermore,  there  have  been  few 
attempts  to  generalize  and  to  group  examples  of  typical 
phenomena  in  such  a  manner  as  to  enable  a  general 
reader  to  see  the  complex  fabric  as  a  whole.  Finally, 
the  occurrence  and  application  of  illusions  in  various 
arts  and  the  prominence  of  illusions  on  every  hand 
have  not  been  especially  treated.  It  is  the  hope  that 
this  will  be  realized  in  the  following  chapters  in  so 
far  as  brevity  of  treatment  makes  this  possible. 

Doubtless  thoughtful  observers  ages  ago  noticed 
visual  illusions,  especially  those  found  in  nature  and 
in  architecture.  When  it  is  considered  that  geometrical 
figures  are  very  commonly  of  an  illusory  character  it 
appears  improbable  that  optical  illusions  could  have 
escaped  the  keenness  of  Euclid.  The  apparent  en- 
largement of  the  moon  near  the  horizon  and  the  ap- 
parent flattened  vault  of  the  sky  were  noticed  at  least 
a  thousand  years  ago  and  literature  yields  several 
hundred  memoirs  on  these  subjects.  One  of  the  oldest 
dissertations  upon  the  apparent  form  of  the  sky  was 
published  by  Alhazen,  an  Arab  astronomer  of  the 
tenth  century.  Kepler  in  1618  wrote  upon  the 
subject. 

Philosophers  of  the  past  centuries  prepared  the 


INTRODUCTION  9 


way  toward  an  understanding  of  many  complexities 
of  today.  They  molded  thought  into  correct  form  and 
established  fundamental  concepts  and  principles.  Their 
chief  tool  was  philosophy,  the  experimental  attack 
being  left  to  the  scientists  of  the  modern  age.  How- 
ever, they  established  philosophically  such  principles 
as  "  space  and  time  are  not  realities  of  the  phenomenal 
world  but  the  modes  under  which  we  see  things  apart." 
As  science  became  organized  during  the  present  ex- 
perimental era,  measurements  were  applied  and  there 
began  to  appear  analytical  discussions  of  various  sub- 
jects including  optical  illusions.  One  of  the  earliest 
investigations  of  the  modern  type  was  made  by  Oppel, 
an  account  of  which  appeared  in  1854.  Since  that 
time  scientific  literature  has  received  thousands  of 
worthy  contributions  dealing  with  visual  illusions. 

There  are  many  facts  affecting  vision  regarding 
which  no  theory  is  necessary.  They  speak  for  them- 
selves. There  are  many  equally  obvious  facts  which 
are  not  satisfactorily  explained  but  the  lack  of  ex- 
planation does  not  prevent  their  recognition.  In 
fact,  only  the  scientist  needs  to  worry  over  systematic 
explanations  and  theoretical  generalizations.  He  needs 
these  in  order  to  invade  and  to  explore  the  other  un- 
knowns where  he  will  add  to  his  storehouse  of  knowl- 
edge. A  long  step  toward  understanding  is  made  by 
becoming  acquainted  with  certain  physical,  physio- 
logical, and  psychological  facts  of  light,  color,  and 
lighting.  Furthermore,  acquaintance  with  the  visual 
process  and  with  the  structure  of  the  eye  aids  materi- 
ally. For  this  reason  the  next  two  chapters  have  been 
added  even  at  the  risk  of  discouraging  some  readers. 


10  VISUAL  ILLUSIONS 

In  a  broad  sense,  any  visual  perception  which  does 
not  harmonize  with  physical  measurements  may  be 
termed  an  "  illusion."  Therefore,  the  term  could 
include  those  physical  illusions  obtained  by  means  of 
prisms,  lenses,  and  mirrors  and  such  illusions  as  the 
mirage.  It  could  also  include  the  physiological  illu- 
sions of  light  and  color  such  as  after-images,  irradia- 
tion, and  contrast,  and  the  psycho-physiological  illu- 
sions of  space  and  the  character  of  objects.  In  fact, 
the  scope  of  the  following  chapters  is  arbitrarily  ex- 
tended to  include  all  these  aspects,  but  confines  con- 
sideration only  to  "  static  "  illusions. 

In  a  more  common  sense  attention  is  usually 
restricted  to  the  last  group;  that  is,  to  the  psycho- 
physiological  illusions  attending  the  perception  of 
space  and  the  character  of  objects  although  motion 
is  often  included.  It  should  be  obvious  that  no  simple 
or  even  single  theory  can  cover  the  vast  range  of  illu- 
sions considered  in  the  broad  sense  because  there 
are  so  many  different  kinds  of  factors  involved.  For 
this  reason  explanations  will  be  presented  wherever 
feasible  in  connection  with  specific  illusions.  How- 
ever, in  closing  this  chapter  it  appears  of  interest  to 
touch  upon  the  more  generally  exploited  theories  of 
illusions  of  the  type  considered  in  the  foregoing  re- 
stricted sense.  Hypotheses  pertaining  to  illusions  are 
generally  lacking  in  agreement,  but  for  the  special 
case  of  what  might  be  more  safely  termed  "  geometrical- 
optical  illusions  "  two  different  theories,  by  Lipps  and 
by  Wundt  respectively,  are  conspicuous.  In  fact,  most 
theories  are  variants  of  these  two  systematic  "  ex- 
planations "  of  illusions  (in  the  restricted  sense). 


INTRODUCTION  11 


Lipps  proposed  the  principle  of  mechanical-esthetic 
unity,  according  to  which  we  unconsciously  give  to 
every  space-form  a  living  personality  and  uncon- 
sciously consider  certain  mechanical  forces  acting. 
Our  judgments  are  therefore  modified  by  this  an- 
thropomorphic attitude.  For  example,  we  regard  the 
circle  as  being  the  result  of  the  action  of  tangential 
and  radial  forces  in  which  the  latter  appear  to  tri- 
umph. According  to  Lipps'  theory  the  circle  has  a 
centripetal  character  and  these  radial  forces  toward 
the  center,  which  apparently  have  overcome  the 
tangential  forces  during  the  process  of  creating  the 
circle,  lead  to  underestimation  of  its  size  as  compared 
with  a  square  of  the  same  height  and  breadth.  By 
drawing  a  circle  and  square  side  by  side,  with  the 
diameter  of  the  former  equal  to  the  length  of  a  side 
of  the  latter,  this  illusion  is  readily  demonstrated. 
Of  course,  the  square  has  a  greater  area  than  the 
circle  and  it  is  difficult  to  determine  the  effect  of  this 
disparity  in  area.  Figure  60  where  the  areas  of  the 
circle  and  square  are  equal  and  consequently  the 
height  of  the  former  is  considerably  greater  than  the 
latter,  is  of  interest  in  this  connection.  By  experi- 
menting with  a  series  of  pairs  consisting  of  a  circle 
and  a  square,  varying  in  dimensions  from  equal  heights 
to  equal  areas,  an  idea  of  the  "  shrinking  "  character 
of  the  circle  becomes  quite  apparent. 

Wundt  does  not  attribute  the  illusion  to  a  decep- 
tion or  error  of  judgment  but  to  direct  perception. 
According  to  his  explanation,  the  laws  of  retinal  image 
(fixation)  and  eye-movement  are  responsible.  For 
example,  vertical  distances  appear  greater  than  hori- 


12  VISUAL  ILLUSIONS 

zontal  ones  because  the  effort  or  expenditure  of  energy 
is  greater  in  raising  the  eyes  than  in  turning  them 
through  an  equal  angle  in  a  horizontal  plane.  Un- 
conscious or  involuntary  eye-movements  also  appear 
to  play  a  part  in  many  linear  or  more  accurately, 
angular  illusions,  but  certainly  Wundt's  explanation 
does  not  suffice  for  all  illusions  although  it  may  ex- 
plain many  geometrical  illusions.  It  may  be  said  to 
be  of  the  "  perceptive  "  class  and  Lipps'  theory  to  be 
of  the  "  judgment  "  or  "  higher-process  "  class.  As 
already  stated,  most  of  the  other  proposed  explanations 
of  geometrical  illusions  may  be  regarded  as  being 
related  to  one  of  these  two  theories.  There  is  the 
"indistinct  vision"  theory  of  Einthoven;  the  "per- 
spective "  theory  of  Hering,  Guye,  Thiery,  and  others ; 
the  "  contrast "  theory  of  Helmholtz,  Loeb,  and  Hey- 
man;  and  the  "  contrast-con/?uxion  "  theory  of  Miiller- 
Lyer.  In  order  not  to  discourage  the  reader  at  the 
outset,  theories  as  such  will  be  passed  by  with  this 
brief  glimpse.  However,  more  or  less  qualified  ex- 
planations are  presented  occasionally  in  some  of  the 
chapters  which  follow  in  order  to  indicate  or  to  sug- 
gest a  train  of  thought  should  the  reader  desire  to 
attempt  to  understand  some  of  the  numerous  inter- 
esting illusions. 


n 

THE  EYE 

HELMHOLTZ,  who  contributed  so  much  toward 
our  knowledge  of  the  visual  process,  in  referring 
to  the  eye,  once  stated  that  he  could  make  a 
much  better  optical  instrument  but  not  a  better  eye. 
In  other  words,  the  eye  is  far  from  an  ideal  optical 
instrument  but  as  an  eye  it  is  wonderful.  Its  range 
of  sensitiveness  and  its  adaptability  to  the  extreme 
variety  of  demands  upon  it  are  truly  marvelous  when 
compared  with  instruments  devised  by  mankind. 
Obviously,  the  eye  is  the  connecting  link  between 
objective  reality  and  visual  perception  and,  therefore, 
it  plays  an  important  part  in  illusions.  In  fact,  some- 
times it  is  solely  responsible  for  the  illusion.  The 
process  of  vision  may  be  divided  into  several  steps 
such  as  (1)  the  lighting,  color,  character,  and  dispo- 
sition of  objects;  (2)  the  mechanism  by  which  the 
image  is  formed  upon  the  retina;  (3)  various  optical 
defects  of  this  mechanism;  (4)  the  sensitiveness  of 
the  parts  of  the  retina  to  light  and  color ;  (5)  the  struc- 
ture of  the  retina ;  (6)  the  parts  played  by  monocular 
and  binocular  vision;  and  (7)  the  various  events 
which  follow  the  formation  of  the  image  upon  the 
retina. 

The  mechanism  of  the  eye  makes  it  possible  to  see 
not  only  light  but  objects.     Elementary  eyes  of  the 

13 


VISUAL  ILLUSIONS 


lowest  animals  perceive  light  but  cannot  see  objects. 
These  eyes  are  merely  specialized  nerves.  In  the 
human  eye  the  optic  nerve  spreads  to  form  the  retina 
and  the  latter  is  a  specialized  nerve.  Nature  has 
accompanied  this  evolution  by  developing  an  instru- 
ment —  the  eye  —  for  intensifying  and  defining  and 
the  whole  is  the  visual  sense-organ.  The  latter 
contains  the  most  highly  specialized  nerve  and  the 

most  refined  physio- 
logical mechanism, 
the  result  being  the 
highest  sense-organ. 
The  eye  is  approx- 
imately a  spherical 
shell  transparent  at 
the  front  portion  and 
opaque  (or  nearly  so) 
over  the  remaining 
eighty  per  cent  of  its 
surface.  The  optical 
path  consists  of  a 
series  of  transparent 
liquids  and  solids. 
The  chief  details  of 
the  structure  of  the  eye  are  represented  in  Fig.  1. 
Beginning  with  the  exterior  and  proceeding  toward  the 
retina  we  find  in  succession  the  cornea,  the  anterior 
chamber  containing  the  aqueous  humor,  the  iris,  the 
lens,  the  large  chamber  containing  the  vitreous  humor, 
and  finally  the  retina.  Certain  muscles  alter  the  posi- 
tion of  the  eye  and  consequently  the  optical  axis,  and 
focusing  (accommodation)  is  accomplished  by  altering 


Fig.  1. — Principal  parts  of  the  eye. 

A,  Conjunctiva ;*B,  Retina;  C,  Choroid;  D,  Sclera; 
E,  Fovea;  F,  Blind  Spot;  G,  Optic  Nerve;  H, 
Ciliary  Muscle;  I,  Iris;  J,  Cornea;  K,  Ligament. 


THE  EYE  16 


the  thickness  and  shape,  and  consequently  the  focal 
length,  of  the  lens. 

The  iris  is  a  shutter  which  automatically  controls 
to  some  degree  the  amount  of  light  reaching  the 
retina,  thereby  tending  to  protect  the  latter  from  too 
much  light.  It  also  has  some  influence  upon  the  defini- 
tion of  the  image ;  that  is,  upon  what  is  termed  "  visual 
acuity  "  or  the  ability  to  distinguish  fine  detail.  It  is 
interesting  to  compare  the  eye  with  the  camera.  In 
the  case  of  the  camera  and  the  photographic  process, 
we  have  (1)  an  inverted  light-image,  a  facsimile  of 
the  object  usually  diminished  in  size;  (2)  an  in- 
visible image  in  the  photographic  emulsion  consisting 
of  molecular  changes  due  to  light ;  and  (3)  a  visible 
image  developed  on  the  plate.  In  the  case  of  the  eye 
and  the  visual  process  we  have  (1)  an  inverted  light- 
image,  a  facsimile  of  the  object  diminished  in  size; 
(2)  the  invisible  image  in  the  retinal  substances  prob- 
ably consisting  of  molecular  changes  due  to  light;' 
and  (3)  an  external  visible  image.  It  will  be  noted 
that  in  the  case  of  vision  the  final  image  is  projected 
outward  —  it  is  external.  The  more  we  think  of  this 
outward  projection  the  more  interesting  and  marvel- 
ous vision  becomes.  For  example,  it  appears  certain 
that  if  a  photographic  plate  could  see  or  feel,  it  would 
see  or  feel  the  silver  image  upon  itself  but  not  out 
in  space.  However,  this  point  is  discussed  further 
in  the  next  chapter. 

In  the  camera  and  photographic  process  we  trace 
mechanism,  physics,  and  chemistry  throughout.  In 
the  eye  and  visual  process  we  are  able  to  trace  these 
factors  only  to  a  certain  point,  where  we  encounter 


16  VISUAL  ILLUSIONS 

the  super-physical  and  super-chemical.  Here  molecu- 
lar change  is  replaced  by  sensation,  perception,  thought, 
and  emotion.  Our  exploration  takes  us  from  the  phys- 
ical world  into  another,  wholly  different,  where  there 
reigns  another  order  of  phenomena.  We  have  passed 
from  the  material  into  the  mental  world. 

The  eye  as  an  optical  mechanism  is  reducible  to  a 
single  lens  and  therefore  the  image  focused  upon  the 
retina  is  inverted.  However,  there  is  no  way  for  the 
observer  to  be  conscious  of  this  and  therefore  the 
inverted  image  causes  no  difficulty  in  seeing.  The 
images  of  objects  in  the  right  half  of  the  field  of  view 
are  focused  upon  the  left  half  of  the  retina.  Similarly, 
the  left  half  of  the  field  of  view  corresponds  to  the 
right  half  of  the  retina;  the  upper  half  of  the  former 
to  the  lower  half  of  the  latter;  and  so  on.  When  a 
ray  of  light  from  an  object  strikes  the  retina  the  im- 
pression  is  referred  back  along  the  ray-line  into  the 
original  place  in  space.  This  is  interestingly  demon- 
strated in  a  simple  manner.  Punch  a  pin-hole  in  a  card 
and  hold  it  about  four  inches  from  the  eye  and  at  the 
same  time  hold  a  pin-head  as  close  to  the  cornea  as 
possible.  The  background  for  the  pin-hole  should  be 
the  sky  or  other  bright  surface.  After  a  brief  trial  an 
inverted  image  of  the  pin-head  is  seen  in  the  hole. 
Punch  several  holes  in  the  card  and  in  each  will  be 
seen  an  inverted  image  of  the  pin-head. 

The  explanation  of  the  foregoing  is  not  difficult. 
The  pin-head  is  so  close  to  the  eye  that  the  image 
cannot  be  focused  upon  the  retina;  however,  it  is  in 
a  very  favorable  position  to  cast  a  shadow  upon  the 
retina,  the  light-source  being  the  pin-hole  with  a  bright 


THE  EYE  17 


background.  Light  streaming  through  the  pin-hole 
into  the  eye  casts  an  erect  shadow  of  the  pin-head 
upon  the  retina,  and  this  erect  image  is  projected  into 
space  and  inverted  in  the  process  by  the  effect  of  the 
lens.  The  latter  is  not  operative  during  the  casting 
of  the  shadow  because  the  phi-head  is  too  close  to 
the  lens,  as  already  stated.  It  is  further  proved  to  be 
outward  projection  of  the  retinal  image  (the  shadow) 
because  by  multiplying  the  number  of  pin-holes  (the 
light-sources)  there  are  also  a  corresponding  number 
of  shadows. 

The  foregoing  not  only  illustrates  the  inversion  of 
the  image  but  again  emphasizes  the  fact  that  we  do 
not  see  retinal  images.  Even  the  "  stars  "  which  we 
see  on  pressing  the  eye-lid  or  on  receiving  a  blow  on 
the  eye  are  projected  into  space.  The  "  motes  "  which 
we  see  hi  the  visual  field  while  gazing  at  the  sky  are 
defects  in  the  eye-media,  and  these  images  are  pro- 
jected into  space.  We  do  not  see  anything  in  the  eye. 
The  retinal  image  impresses  the  retina  in  some  definite 
manner  and  the  impression  is  carried  to  the  brain  by 
the  optic  nerve.  The  intellect  then  refers  or  projects 
this  impression  outward  into  space  as  an  external 
image.  ^  The  latter  would  be  a  facsimile  of  the  phys- 
ical object  if  there  were  no  illusions  but  the  fact 
that  there  are  illusions  indicates  that  errors  are 
introduced  somewhere  along  the  path  from  and  to 
the  object. 

It  is  interesting  to  speculate  whether  the  first  visual 
impression  of  a  new-born  babe  is  "projected  out- 
ward "  or  is  perceived  as  in  the  eye.  It  is  equally  futile 
to  conjecture  in  this  manner  because  there  is  no  in- 


18  VISUAL  ILLUSIONS 

dication  that  the  time  will  come  when  the  baby  can 
answer  us  immediately  upon  experiencing  its  first 
visual  impression.  The  period  of  infancy  increases 
with  progress  up  the  scale  of  animal  life  and  this 
lengthening  is  doubtless  responsible  and  perhaps 
necessary  for  the  development  of  highly  specialized 
sense-organs.  Incidentally,  suppose  a  blind  person  to 
be  absolutely  uneducated  by  transferred  experience 
and  that  he  suddenly  became  a  normal  adult  and 
able  to  see.  What  would  he  say  about  his  first  visual 
impression?  Apparently  such  a  subject  is  unobtainable. 
The  nearest  that  such  a  case  had  been  approached  is 
the  case  of  a  person  born  blind,  whose  sight  has  been 
restored.  This  person  has  acquired  much  experience 
with  the  external  world  through  other  senses.  It  has 
been  recorded  that  such  a  person,  after  sight  was 
restored,  appeared  to  think  that  external  objects 
"  touched  "  the  eyes.  Only  through  visual  experience 
is  this  error  in  judgment  rectified. 

Man  studies  his  kind  too  much  apart  from  other 
animals  and  perhaps  either  underestimates  or  over- 
estimates the  amount  of  inherited,  innate,  instinctive 
qualities.  A  new-born  chick  in  a  few  minutes  will  walk 
straight  to  an  object  and  seize  it.  Apparently  this  im- 
plies perception  of  distance  and  direction  and  a  coordi- 
nation of  muscles  for  walking  and  moving  the  eyes. 
It  appears  reasonable  to  conclude  that  a  certain  amount 
of  the  wealth  of  capacities  possessed  by  the  individual 
is  partly  inherited,  and  in  man  the  acquired  predomi- 
nates. But  all  capacities  are  acquired,  for  even  the  in- 
herited was  acquired  in  ancestral  experience.  Even 
instinct  (whatever  that  may  be)  must  involve  inherited 


THE  EYE  19 


experience.  These  glimpses  of  the  depths  to  which 
one  must  dig  if  he  is  to  unearth  the  complete  explana- 
tions of  visual  perception  —  and  consequently  of  illu- 
sions—  indicate  the  futility  of  treating  the  theories 
in  the  available  space  without  encroaching  unduly 
upon  the  aims  of  this  volume. 

Certain  defects  of  the  optical  system  of  the  eye 
must  contribute  toward  causing  illusions.  Any  perfect 
lens  of  homogeneous  material  has  at  least  two  defects, 
known  as  spherical  and  chromatic  aberration.  The 
former  manifests  itself  by  the  bending  of  straight 
lines  and  is  usually  demonstrated  by  forming  an 
image  of  an  object  such  as  a  wire  mesh  or  checker- 
board; the  outer  lines  of  the  image  are  found  to  be 
very  much  bent.  This  defect  in  the  eye-lens  is  some- 
what counteracted  by  a  variable  optical  density,  in- 
creasing from  the  outer  to  the  central  portion.  This 
results  in  an  increase  in  refractive-index  as  the  center 
of  the  lens  is  approached  and  tends  to  diminish  its 
spherical  aberration.  The  eye  commonly  possesses 
abnormalities  such  as  astigmatism  and  eccentricity- 
of  the  optical  elements.  'All  these  contribute  toward 
the  creation  of  illusions. 

White  light  consists  of  rays  of  light  of  various  colors 
and  these  are  separated  by  means  of  a  prism  because 
the  refractive-index  of  the  prism  differs  for  lights  of * 
different  color  or  wave-length.  This  causes  the  blue 
rays,  for  example,  to  be  bent  more  than  the  red  rays 
when  traversing  a  prism.  It  is  in  this  manner  that  the 
spectrum  of  light  may  be  obtained.  A  lens  may  be 
considered  to  be  a  prism  of  revolution  and  it  thus 
becomes  evident  that  the  blue  rays  will  be  brought 


20  VISUAL  ILLUSIONS 

to  a  focus  at  a  lesser  distance  than  the  red  rays ;  that 
is,  the  former  are  bent  more  from  their  original  path 
than  the  latter.  This  defect  of  lenses  is  known  as 
chromatic  aberration  and  is  quite  obvious  in  the  eye. 
It  may  be  demonstrated  by  any  simple  lens,  for  the 
image  of  the  sun,  for  example,  will  appear  to  have  a 
colored  fringe.  A  purple  filter  which  transmits  only 
the  violet  and  red  rays  is  useful  for  this  demonstration. 
By  looking  at  a  lamp-filament  or  candle-flame  some 
distance  away  the  object  will  appear  to  have  a  violet 
halo,  but  the  color  of  the  fringe  will  vary  with  ac- 
commodation. On  looking  through  a  pin-hole  at  the 
edge  of  an  object  silhouetted  against  the  bright  sky 
the  edge  will  appear  red  if  the  light  from  the  pin- 
hole  enters  the  pupil  near  its  periphery.  This  optical 
defect  of  the  eye  makes  objects  appear  more  sharply 
defined  when  viewed  in  monochromatic  light.  In  fact, 
this  is  quite  obvious  when  using  yellow  glasses.  The 
defect  is  also  demonstrated  by  viewing  a  line-spectrum 
focused  on  a  ground  glass.  The  blue  and  red  lines 
cannot  be  seen  distinctly  at  the  same  distance.  The 
blue  lines  can  be  focused  at  a  much  less  distance  than 
the  red  lines.  Chromatic  aberration  can  account  for 
such  an  illusion  as  the  familiar  "  advancing  "  and 
"  retiring  "  colors  and  doubtless  it  plays  a  part  in  many 
illusions. 

The  structure  of  the  retina  plays  a  very  important 
v  part  in  vision  and  accounts  for  various  illusions  and 
many  interesting  visual  phenomena.  The  optic  nerve 
spreads  out  to  form  the  retina  which  constitutes  the 
inner  portion  of  the  spherical  shell  of  the  eye  with  the 
exception  of  the  front  part.  Referring  again  to  Fig.  1, 


THE  EYE  21 


the  outer  coating  of  the  shell  is  called  the  sclerotic. 
This  consists  of  dense  fibrous  tissue  known  as  the 
"  white  of  the  eye."  Inside  this  coating  is  a  layer  of 
black  pigment  cells  termed  the  choroid.  Next  is  the 
bacillary  layer  which  lines  about  five-sixths  of  the 
interior  surface  of  the  eye.  This  is  formed  by  closely 
packed  "  rods  "  and  "  cones,"  which  play  a  dominant 
role  in  the  visual  process.  A  light-sensitive  liquid 
(visual  purple)  and  cellular  and  fibrous  layers  complete 
the  retinal  structure. 

The  place  where  the  optic  nerve  enters  the  eye- 
ball and  begins  to  spread  out  is  blind.  Objects  whose 
images  fall  on  this  spot  are  invisible.  This  blind-spot 
is  not  particularly  of  interest  here,  but  it  may  be  of 
interest  to  note  its  effect.  This  is  easily  done  by 
closing  one  eye  and  looking  directly  at  one  of  two  small 
black  circles  about  two  inches  apart  on  white  paper 
at  a  distance  of  about  a  foot  from  the  eye.  By  moving 
the  objects  about  until  the  image  of  the  circle  not 
directly  looked  at  falls  upon  the  blind-spot,  this  circle 
will  disappear.  A  three-foot  circle  at  a  distance  of  36 
feet  will  completely  disappear  if  its  image  falls  directly 
upon  the  blind-spot.  At  a  distance  of  42  inches  the 
invisible  area  is  about  12  inches  from  the  point  of  sight 
and  about  3  to  4  inches  in  diameter.  At  300  feet  the 
area  is  about  8  feet  in  diameter.  The  actual  size  of 
the  retinal  blind-spot  is  about  0.05  inch  in  diameter 
or  nearly  5  degrees.  Binocular  vision  overcomes  any 
annoyance  due  to  the  blind-spots  because  they  do  not 
overlap  in  the  visual  field.  A  one-eyed  person  is  really 
totally  blind  for  this  portion  of  the  retina  or  of  the 
visual  field. 


22  VISUAL  ILLUSIONS 

The  bacillary  layer  consists  of  so-called  rods  and 
cones.  Only  the  rods  function  under  very  low  in- 
tensities of  illumination  of  the  order  of  moonlight. 
The  cones  are  sensitive  to  color  and  function  only  at 
intensities  greater  than  what  may  be  termed  twilight 
intensities.  These  elements  are  very  small  but  the 
fact  that  they  appear  to  be  connecting  links  between 
the  retinal  image  and  visual  perception,  acuity  or 
discrimination  of  fine  detail  is  limited  inasmuch  as  the 
elements  are  of  finite  dimensions.  The  smallest 
image  which  will  produce  a  visual  impression  is  the 
size  of  the  end  of  a  cone.  The  smallest  distance  be- 
tween two  points  which  is  visible  at  five  inches  is 
about  0.001  inch.  Two  cones  must  be  stimulated  in 
such  a  case.  Fine  lines  may  appear  crooked  because 
of  the  irregular  disposition  of  these  elemental  light- 
sensitive  points.  This  apparent  crookedness  of  lines 
is  an  illusion  which  is  directly  due  to  the  limitations  of 
retinal  elements  of  finite  size. 

The  distribution  of  rods  and  cones  over  the  retina 
is  very  important.  In  the  fovea  centralis  —  the  point 
of  the  retina  on  the  optical  axis  of  the  eye  —  is  a  slight 
depression  much  thinner  than  the  remainder  of  the 
retina  and  this  is  inhabited  chiefly  by  cones.  It  is 
this  spot  which  provides  visual  acuteness.  It  is  easily 
demonstrated  that  fine  detail  cannot  be  seen  well 
defined  outside  this  central  portion  of  the  visual  field. 
When  we  desire  to  see  an  object  distinctly  we  habitu- 
ally  turn  the  head  so  that  the  image  of  the  object 
falls  upon  the  fovea  of  each  eye.  Helmholtz  has 
compared  the  foveal  and  lateral  images  with  a  finished 
drawing  and  a  rough  sketch  respectively. 


THE  EYE  23 


The  fovea  also  contains  a  yellow  pigmentation 
which  makes  this  area  of  the  retina  selective  as  to 
color-vision.  On  viewing  certain  colors  a  difference 
in  color  of  this  central  portion  of  the  field  is  often 
very  evident.  In  the  outlying  regions  of  the  retina, 
rods  predominate  and  in  the  intermediate  zone  both 
rods  and  cones  are  found.  Inasmuch  as  rods  are  not 
sensitive  to  color  and  cones  do  not  function  at  low 
intensities  of  illumination  it  is  obvious  that  visual 
impressions  should  vary,  depending  upon  the  area 
of  the  retina  stimulated.  In  fact,  many  interesting 
illusions  are  accounted  for  in  this  manner,  some  of 
which  are  discussed  later. 

It  is  well  known  that  a  faint  star  is  seen  best  by 
averted  vision.  It  may  be  quite  invisible  when  the 
eye  is  directed  toward  it,  that  is,  when  its  image 
falls  upon  the  rod-free  fovea.  However,  by  averting 
the  line  of  sight  slightly,  the  image  is  caused  to  fall 
on  a  retinal  area  containing  rods  (sensitive  to  feeble 
light)  and  the  star  may  be  readily  recognized.  The 
fovea  is  the  point  of  distinct  focus.  It  is  necessary 
for  fixed  thoughtful  attention.  It  exists  in  the  retina 
of  man  and  of  higher  monkeys  but  it  quickly  disap- 
pears as  we  pass  down  the  scale  of  animal  life.  It 
may  be  necessary  for  the  safety  of  the  lower  animals 
that  they  see  equally  well  over  a  large  field;  however, 
it  appears  advantageous  that  man  give  fixed  and 
undivided  attention  to  the  object  looked  at.  Man 
does  not  need  to  trust  solely  to  his  senses  to  protect 
himself  from  dangers.  He  uses  his  intellect  to  in- 
vent and  to  construct  artificial  defenses.  Without 
the  highly  specialized  fovea  we  might  see  equally 


24  VISUAL  ILLUSIONS 

well  over  the  whole  retina  but  could  not  look  atten- 
tively at  anything,  and  therefore  could  not  observe 
thoughtfully. 

When  an  image  of  a  bright  object  exists  upon  the 
retina  for  a  time  there  results  a  partial  exhaustion  or 
fatigue  of  the  retinal  processes  with  a  result  that  an 
after-image  is  seen.  This  after-image  may  be  bright 
for  a  time  owing  to  the  fact  that  it  takes  time  for 
the  retinal  process  to  die  out.  Then  there  comes 
a  reaction  which  is  apparent  when  the  eye  is  di- 
rected toward  illuminated  surfaces.  The  part  of  the 
retina  which  has  been  fatigued  does  not  respond  as 
fully  as  the  fresher  areas,  with  the  result  that  the 
fatigued  area  contributes  a  darker  area  in  the  visual 
field.  This  is  known  as  an  after-image  and  there 
are  many  interesting  variations. 

The  after-image  usually  undergoes  a  series  of 
changes  in  color  as  well  as  in  brightness  as  the  retinal 
process  readjusts  itself.  An  after-image  of  a  colored 
object  may  often  appear  of  a  color  complementary  to 
the  color  of  the  object.  This  is  generally  accounted 
for  by  fatigue  of  the  retinal  processy  There  are  many 
conflicting  theories  of  color-vision  but  they  are  not 
as  conflicting  in  respect  to  the  aspect  of  fatigue  as 
in  some  other  aspects.  If  the  eye  is  directed  toward 
a  green  surface  for  a  time  and  then  turned  toward  a 
white  surface,  the  fatigue  to  green  light  diminishes 
the  extent  of  response  to  the  green  rays  in  the  light 
reflected  by  the  white  surface.  The  result  is  the 
perception  of  a  certain  area  of  the  white  surface 
(corresponding  to  the  portion  of  the  field  fatigued 
by  green  light)  as  of  a  color  equal  to  white  minus 


THE  EYE  25 


some  green — the  result  of  which  is  pink  or  purple. 
This  is  easily  understood  by  referring  to  the  prin- 
ciples of  color-mixture.  Red,  green,  and  blue  (or 
violet)  mixed  in  proper  proportions  will  produce  any 
color  or  tint  and  even  white.  Thus  these  may  be 
considered  to  be  the  components  of  white  light.  Hence 
if  the  retina  through  fatigue  is  unable  to  respond 
fully  to  the  green  component,  the  result  may  be  ex- 
pressed mathematically  as  red  plus  blue  plus  reduced 
green,  or  synthetically  a  purplish  white  or  pink.  When 
fatigued  to  red  light  the  after-image  on  a  white  surface 
is  blue-green.  When  fatigued  to  blue  light  it  is  yel- 
lowish. 

Further  mixtures  may  be  obtained  by  directing 
the  after-image  upon  colored  surfaces.  In  this  man- 
ner many  of  the  interesting  visual  phenomena  and 
illusions  associated  with  the  viewing  of  colors  are 
accounted  for.  The  influence  of  a  colored  environ- 
ment upon  a  colored  object  is  really  very  great.  This 
is  known  as  simultaneous  contrast.  The  influence 
of  the  immediately  previous  history  of  the  retina 
upon  the  perception  of  colored  surfaces  is  also  very 
striking.  This  is  called  successive  contrast.  It  is 
interesting  to  note  that  an  after-image  produced 
by  looking  at  a  bright  light-source,  for  example,  is 
projected  into  space  even  with  the  eyes  closed.  It 
is  instructive  to  study  after-images  and  this  may  be 
done  at  any  moment.  On  gazing  at  the  sun  for  an 
instant  and  then  looking  away,  an  after-image  is  seen 
which  passes  in  color  from  green,  blue,  purple,  etc., 
and  finally  fades.  For  a  time  it  is  brighter  than  the 
background  which  may  conveniently  be  the  sky.  On 


26  VISUAL  ILLUSIONS 

closing  the  eyes  and  placing  the  hands  over  them  the 
background  now  is  dark  and  the  appearance  of  the 
after-image  changes  markedly.  There  are  many 
kinds,  effects,  and  variations  of  after-images,  some 
of  which  are  discussed  in  other  chapters. 

As  the  intensity  of  illumination  of  a  landscape, 
for  example,  decreases  toward  twilight,  the  retina 
diminishes  in  sensibility  to  the  rays  of  longer  wave- 
lengths such  as  yellow,  orange,  and  red.  Therefore, 
it  becomes  relatively  more  sensitive  to  the  rays  of 
shorter  wave-length  such  as  green,  blue,  and  violet. 
The  effects  of  this  Purkinje  phenomenon  (named 
after  the  discoverer)  may  be  added  to  the  class  of 
illusions  treated  in  this  book.  It  is  interesting  to 
note  in  this  connection  that  moonlight  is  represented 
on  some  paintings  and  especially  on  the  stage  as 
greenish  blue  in  color,  notwithstanding  that  physical 
measurements  show  it  to  be  approximately  the  color 
of  sunlight.  In  fact,  it  is  sunlight  reflected  by  dead, 
frigid,  and  practically  colorless  matter. 

Some  illusions  may  be  directly  traced  to  the 
structure  of  the  eye  under  unusual  lighting  conditions. 
For  example,  in  a  dark  room  hold  a  lamp  obliquely 
outward  but  near  one  eye  (the  other  being  closed 
and  shielded)  and  forward  sufficiently  for  the  retina 
to  be  strongly  illuminated.  Move  the  lamp  gently 
while  gazing  at  a  plain  dark  surface  such  as  the  wall. 
Finally  the  visual  field  appears  dark,  due  to  the  in- 
tense illumination  of  the  retina  and  there  will  appear, 
apparently  projected  upon  the  wall,  an  image  re- 
sembling a  branching  leafless  tree.  These  are  really 
shadows  of  the  blood  vessels  in  the  retina.  The 


THE  EYE  27 


experiment  is  more  successful  if  an  image  of  a 
bright  light-source  is  focused  on  the  sclerotic  near 
the  cornea.  If  this  image  of  the  light-source  is 
moved,  the  tree-like  image  seen  in  the  visual  field 
will  also  move. 

The  rate  of  growth  and  decay  of  various  color- 
sensations  varies  considerably.  By  taking  advantage 
of  this  fact  many  illusions  can  be  produced.  In 
fact,  the  careful  observer  will  encounter  many 
illusions  which  may  be  readily  accounted  for  in  this 
manner. 

It  may  be  said  that  in  general  the  eyes  are  never 
at  rest.  Involuntary  eye-movements  are  taking  place  ' 
all  the  time,  at  least  during  consciousness.  Some 
have  given  this  restlessness  a  major  part  in  the  process 
of  vision  but  aside  from  the  correctness  of  theories 
involving  eye-movements,  it  is  a  fact  that  they  are 
responsible  for  certain  illusions.  On  a  star-lit  night 
if  one  lies  down  and  looks  up  at  a  star  the  latter  will 
be  seen  to  appear  to  be  swimming  about  more  or 
less  jerkily.  On  viewing  a  rapidly  revolving  wheel 
of  an  automobile  as  it  proceeds  down  the  street, 
occasionally  it  will  be  seen  to  cease  revolving  mo- 
mentarily. These  apparently  are  accounted  for  by  - 
involuntary  eye-movements  which  take  place  regard- 
less of  the  effort  made  to  fixate  vision. 

If  the  eyelids  are  almost  closed,  streamers  ap- 
pear to  radiate  in  various  directions  from  a  light- 
source.  Movements  of  the  eyelids  when  nearly 
closed  sometimes  cause  objects  to  appear  to  move. 
These  may  be  accounted  for  perhaps  by  the  dis- 
tortion of  the  moist  film  which  covers  the  cornea. 


28  VISUAL  ILLUSIONS 

The  foregoing  are  only  a  few  of  the  many  visual 
phenomena  due  largely  to  the  structure  of  the  eye. 
The  effects  of  these  and  many  others  enter  into  visual 
illusions,  as  will  be  seen  here  and  there  throughout 
the  chapters  which  follow. 


Ill 

VISION 

A  DESCRIPTION  of  the  eye  by  no  means  suf- 
fices to  clarify  the  visual  process.  Even  the 
descriptions  of  various  phenomena  in  the  pre- 
ceding chapter  accomplish  little  more  than  to  ac- 
quaint the  reader  with  the  operation  of  a  mechanism, 
although  they  suggest  the  trend  of  the  explanations 
of  many  illusions.  At  best  only  monocular  vision 
has  been  treated,  and  it  does  not  exist  normally  for 
human  beings.  A  person  capable  only  of  monocular 
vision  would  be  like  Cyclops  Polyphemus.  We  might 
have  two  eyes,  or  even,  like  Argus,  possess  a  hundred 
eyes  and  still  not  experience  the  wonderful  advan- 
tages of  binocular  vision,  for  each  eye  might  see  in- 
dependently. The  phenomena  of  binocular  vision 
are  far  less  physical  than  those  of  monocular  vision. 
They  are  much  more  obscure,  illusory,  and  perplexing 
because  they  are  more  complexly  interwoven  with  or 
allied  to  psychological  phenomena. 

The  sense  of  sight  differs  considerably  from  the 
other  senses.  The  sense  of  touch  requires  solid  con- 
tact (usually);  taste  involves  liquid  contact;  smell, 
gaseous  contact;  and  hearing  depends  upon  a  relay 
of  vibrations  from  an  object  through  another  medium 
(usually  air),  resulting  finally  in  contact.  However, 
we  perceive  things  at  a  distance  through  vibration 

29 


30  VISUAL  ILLUSIONS 

(electromagnetic  waves  called  light)  conveyed  by  a 
subtle,  intangible,  universal  medium  which  is  un- 
recognizable excepting  as  a  hypothetically  necessary 
bearer  of  light-waves  or,  more  generally,  radiant 
energy. 

It  also  is  interesting  to  compare  the  subjective- 
ness  and  objectiveness  of  sensations.  The  sensation 
of  taste  is  subjective ;  it  is  in  us,  not  in  the  body  tasted. 
In  smell  we  perceive  the  sensation  in  the  nose  and  by 
experience  refer  it  to  an  object  at  a  distance.  The 
sensation  of  hearing  is  objective;  that  is,  we  refer 
the  cause  to  an  object  so  completely  that  there  is 
practically  no  consciousness  of  sensation  in  the  ear. 
In  sight  the  impression  is  so  completely  projected  out- 
ward into  space  and  there  is  so  little  consciousness 
of  any  occurrence  in  the  eye  that  it  is  extremely  dif- 
ficult to  convince  ourselves  that  it  is  essentially  a 
subjective  sensation.  The  foregoing  order  repre- 
sents the  sense-organs  in  increasing  specialization 
and  refinement  In  the  two  higher  senses  —  sight 
and  hearing  —  there  is  no  direct  contact  with  the 
object  and  an  intricate  mechanism  is  placed  in  front 
of  the  specialized  nerve  to  define  and  to  intensify  the 
impression.  In  the  case  of  vision  this  highly  developed 
instrument  makes  it  possible  to  see  not  only  light  but 
objects. 

As  we  go  up  the  scale  of  vertebrate  animals  we 
find  that  there  is  a  gradual  change  of  the  position  of 
the  eyes  from  the  sides  to  the  front  of  the  head  and 
a  change  of  the  inclination  of  the  optical  axes  of  the 
two  eyes  from  180  degrees  to  parallel.  There  is  also 
evident  a  gradual  increase  in  the  fineness  of  the 


VISION  31 


bacillary  layer  of  the  retina  from  the  margins  toward 
the  center,  and,  therefore,  an  increasing  accuracy  in 
the  perception  of  form.  This  finally  results  in  a  highly 
organized  central  spot  or  fovea  which  is  possessed 
only  by  man  and  the  higher  monkeys.  Proceeding 
up  the  scale  we  also  find  an  increasing  ability  to  con- 
verge the  optic  axes  on  a  near  point  so  that  the  images 
of  the  point  may  coincide  with  the  central  spots  of  both 
retinas.  These  changes  and  others  are  closely  as- 
sociated with  each  other  and  especially  with  the 
development  of  the  higher  faculties  of  the  mind. 

Binocular  vision  in  man  and  in  the  higher  animals 
is  the  last  result  of  the  gradual  improvement  of  the 
most  refined  sense-organ,  adapting  it  to  meet  the 
requirements  of  highly  complex  organisms.  It  can- 
not exist  in  some  animals,  such  as  birds  and  fishes, 
because  they  cannot  converge  their  two  optical  axes 
upon  a  near  point.  When  a  chicken  wishes  to  look 
intently  at  an  object  it  turns  its  head  and  looks  with 
one  eye.  Such  an  animal  sees  with  two  eyes  in- 
dependently and  possibly  moves  them  independently. 
The  normal  position  of  the  axes  of  human  eyes  is 
convergent  or  parallel  but  it  is  possible  to  diverge 
the  axes.  In  fact,  with  practice  it  is  possible  to  di- 
verge the  axes  sufficiently  to  look  at  a  point  near  the 
back  of  the  head,  although,  of  course,  we  do  not 
see  the  point. 

The  movement  of  the  eyes  is  rather  complex. 
When  they  move  together  to  one  side  or  the  other 
or  up  and  down  in  a  vertical  plane  there  is  no  rotation 
of  the  optical  axes;  that  is,  no  torsion.  When  the 
visual  plane  is  elevated  and  the  eyes  move  to  the 


32  VISUAL  ILLUSIONS 

right  they  rotate  to  the  right;  when  they  move  to 
the  left  they  rotate  to  the  left.  When  the  visual  plane 
is  depressed  and  the  eyes  move  to  the  right  they 
rotate  to  the  left;  when  they  move  to  the  left  they 
rotate  to  the  right.  Through  experience  we  uncon- 
sciously evaluate  the  muscular  stresses,  efforts,  and 
movements  accompanying  the  motion  of  the  eyes 
and  thereby  interpret  much  through  visual  percep- 
tion in  regard  to  such  aspects  of  the  external  world 
as  size,  shape,  and  distance  of  objects.  Even  this 
brief  glimpse  of  the  principal  movements  of  the  eyes 
indicates  a  complexity  which  suggests  the  intricacy 
of  the  explanations  of  certain  visual  phenomena. 

At  this  point  it  appears  advantageous  to  set  down 
the  principal  modes  by  which  we  perceive  the  third 
dimension  of  space  and  of  objects  and  other  aspects 
of  the  external  world.  They  are  as  follows:  (1)  ex- 
tent; (2)  clearness  of  brightness  and  color  as  af- 
fected by  distance;  (3)  interference  of  near  objects 
with  those  more  distant;  (4)  elevation  of  objects; 
(5)  variation  of  light  and  shade  on  objects;  (6)  cast 
shadows;  (7)  perspective;  (8)  variation  of  the  visor 
angle  in  proportion  to  distance;  (9)  muscular  effort 
attending  accommodation  of  the  eye ;  (10)  stereoscopic 
vision;  (11)  muscular  effort  attending  convergence 
of  the  axes  of  the  eyes.  It  will  be  recognized  that 
only  the  last  two  are  necessarily  concerned  with 
binocular  vision.  These  varieties  of  experiences 
may  be  combined  in  almost  an  infinite  variety  of 
proportions. 

Wundt  in  his  attempt  to  explain  visual  percep- 
tion considered  chiefly  three  factors:  (1)  the  retinal 


VISION  33 


image  of  the  eye  at  rest;  (2)  the  influence  of  the  move- 
ments of  one  eye ;  and,  (3)  the  additional  data  fur- 
nished by  the  two  eyes  functioning  together.  There 
are  three  fields  of  vision  corresponding  to  the  fore- 
going. These  are  the  retinal  field  of  vision,  the  mo- 
nocular field,  and  the  binocular  field.  The  retinal 
field  of  vision  is  that  of  an  eye  at  rest  as  compared 
with  the  monocular  field,  which  is  all  that  can  be  seen 
with  one  eye  hi  its  entire  range  of  movement  and 
therefore  of  experience.  The  retinal  field  has  no 
clearly  defined  boundaries  because  it  finally  fades 
at  its  indefinite  periphery  into  a  region  where  sensa- 
tion ceases. 

It  might  be  tiresome  to  follow  detailed  analyses 
of  the  many  modes  by  which  visual  perception  is 
attained,  so  only  a  few  generalizations  will  be  pre- 
sented. For  every  voluntary  act  of  sight  there  are 
two  adjustments  of  the  eyes,  namely,  focal  and  axial. 
In  the  former  case  the  ciliary  muscle  adjusts  the  lens 
in  order  to  produce  a  defined  image  upon  the  retina. 
In  axial  adjustments  the  two  eyes  are  turned  by 
certain  muscles  so  that  their  axes  meet  on  the  object 
looked  at  and  the  images  of  the  object  fall  on  the 
central-spots  of  the  retina.  These  take  place  together 
without  distinct  volition  for  each  but  by  the  single 
voluntary  act  of  looking.,  Through  experience  the  in- 
tellect has  acquired  a  wonderful  capacity  to  interpret 
such  factors  as  size,  form,  and  distance  in  terms  of 
the  muscular  movements  in  general  without  the  ob- 
server being  conscious  of  such  interpretations. 

Binocular  vision  is  easily  recognized  by  holding  a 
finger  before  the  eyes  and  looking  at  a  point  beyond 


34  VISUAL  ILLUSIONS 

it.  The  result  is  two  apparently  transparent  fingers. 
An  object  is  seen  single  when  the  two  retinal  images 
fall  on  corresponding  points.  Direction  is  a  primary 
datum  of  sense.  The  property  of  corresponding  points 
of  the  two  retinas  (binocular  vision)  and  consequently 
of  identical  spatial  points  in  the  two  visual  fields  is 
not  so  simple.  It  is  still  a  question  whether  corre- 
sponding points  (that  is,  the  existence  of  a  correspond- 
ing point  in  one  retina  for  each  point  in  the  other 
retina)  are  innate,  instinctive,  and  are  antecedent 
of  experience  or  are  "  paired  "  as  the  result  of  ex- 
perience. The  one  view  results  in  the  nativistic,  the 
other  in  the  empiristic  theory.  Inasmuch  as  some 
scientists  are  arrayed  on  one  side  and  some  on  the 
other,  it  appears  futile  to  dwell  further  upon  this 
aspect.  It  must  suffice  to  state  that  binocular  vision, 
which  consists  of  two  retinas  and  consequently  two 
fields  of  view  absolutely  coordinated  in  some  manner 
in  the  brain,  yields  extensive  information  concerning 
space  and  its  contents. 

After  noting  after-images,  motes  floating  in  the 
field  of  view  (caused  by  defects  in  the  eye-media) 
and  various  other  things,  it  is  evident  that  what  we 
call  the  field  of  view  is  the  external  projection  into 
space  of  retinal  states.  All  the  variations  of  the 
latter,  such  as  images  and  shadows  which  are  pro- 
duced in  the  external  field  of  one  eye,  are  faithfully 
reproduced  in  the  external  field  of  the  other  eye. 
This  sense  of  an  external  visual  field  is  ineradicable. 
Even  when  the  eyes  are  closed  the  external  field  is 
still  there;  the  imagination  or  intellect  projects  it 
outward.  Objects  at  different  distances  cannot  be 


VISION  35 


seen  distinctly  at  the  same  time  but  by  interpreting 
the  eye-movements  as  the  point  of  sight  is  run  back- 
ward and  forward  (varying  convergence  of  the  axes) 
the  intellect  practically  automatically  appraises  the 
size,  form,  and  distance  of  each  object.  Obviously, 
experience  is  a  prominent  factor.  The  perception  of 
the  third  dimension,  depth  or  relative  distance,  whether 
in  a  single  object  or  a  group  of  objects,  is  the  result 
of  the  successive  combination  of  the  different  parts 
of  two  dissimilar  images  of  the  object  or  group. 

As  already  stated,  the  perception  of  distance,  size, 
and  form  is  based  partly  upon  monocular  and  partly 
upon  binocular  vision,  and  the  simple  elements  upon 
which  judgments  of  these  are  based  are  light,  shade, 
color,  intensity,  and  direction.  Although  the  inter- 
pretation of  muscular  adjustments  plays  a  prominent 
part  in  the  formation  of  judgments,  the  influences  of 
mathematical  perspective,  light,  shade,  color,  and  in- 
tensity are  more  direct.  Judgments  based  upon  focal 
adjustment  (monocular)  are  fairly  accurate  at  dis- 
tances from  five  inches  to  several  yards.  Those 
founded  upon  axial  adjustment  (convergence  of  the 
two  axes  in  binocular  vision)  are  less  in  error  than  the 
preceding  ones.  They  are  reliable  to  a  distance  of 
about  1000  feet.  Judgments  involving  mathematical 
perspective  are  of  relatively  great  accuracy  without 
limits.  Those  arrived  at  by  interpreting  aerial  per- 
spective (haziness  of  atmosphere,  reduction  in  color 
due  to  atmospheric  absorption,  etc.)  are  merely 
estimates  liable  to  large  errors,  the  accuracy  depend- 
ing largely  upon  experience  with  local  conditions. 

The  measuring  power  of  the  eye  is  more  liable 


36  VISUAL  ILLUSIONS 

to  error  when  the  distances  or  the  objects  compared 
lie  in  different  directions.  A  special  case  is  the  com- 
parison of  a  vertical  distance  with  a  horizontal  one. 
It  is  not  uncommon  to  estimate  a  vertical  distance 
as  much  as  25  per  cent  greater  than  an  actually  equal 
horizontal  distance.  In  general,  estimates  of  direction 
and  distance  are  comparatively  inaccurate  when  only 
one  eye  is  used  although  a  one-eyed  person  acquires 
unusual  ability  through  a  keener  experience  whetted 
by  necessity.  A  vertical  line  drawn  perpendicular  to 
a  horizontal  one  is  likely  to  appear  bent  when  viewed 
with  one  eye.  Its  apparent  inclination  is  variable  but 
has  been  found  to  vary  from  one  to  three  degrees. 
Monocular  vision  is  likely  to  c^use  straight  lines  to 
appear  crooked,  although  the  "crookedness"  may 
seem  to  be  more  or  less  unstable. 

The  error  in  the  estimate  of  size  is  in  reality  an 
error  in  the  estimation  of  distance  except  in  those 
cases  where  the  estimate  is  based  directly  upon  a  com- 
parison with  an  object  of  supposedly  known  size. 
An  amusing  incident  is  told  of  an  old  negro  who  was 
hunting  for  squirrels.  He  shot  several  times  at  what 
he  supposed  to  be  a  squirrel  upon  a  tree-trunk  and  his 
failure  to  make  a  kill  was  beginning  to  weaken  his 
rather  ample  opinion  of  his  skill  as  a  marksman.  A 
complete  shattering  of  his  faith  in  his  skill  was  only 
escaped  by  the  discovery  that  the  "  squirrel  "  was  a 
louse  upon  his  eyebrow.  Similarly,  a  gnat  in  the  air 
might  appear  to  be  an  airplane  under  certain  favorable 
circumstances.  It  is  interesting  to  note  that  the 
estimated  size  of  the  disk  of  the  sun  or  moon  varies 
from  the  size  of  a  saucer  to  that  of  the  end  of  a  barrel, 


VISION  37 


although  a  pine  tree  at  the  horizon-line  may  be  esti- 
mated as  25  feet  across  despite  the  fact  that  it  may 
be  entirely  included  in  the  disk  of  the  sun  setting 
behind  it. 

Double  images  play  an  important  part  in  the  com- 
parison of  distances  of  objects.  The  "  doubling  "  of 
objects  is  only  equal  to  the  interocular  distance.  Sup- 
pose two  horizontal  wires  or  clotheslines  about  fifty 
feet  away  and  one  a  few  feet  beyond  the  other.  On 
looking  at  these  no  double  images  are  visible  and  it  is 
difficult  or  even  impossible  to  see  which  is  the  nearer 
when  the  points  of  attachment  of  the  ends  are  screened 
from  view.  However,  if  the  head  is  turned  to  one  side 
and  downward  (90  degrees)  so  that  the  interocular 
line  is  now  at  right  angles  (vertical)  to  the  horizontal 
lines,  the  relative  distances  of  the  latter  are  brought 
out  distinctly.  Double  images  become  visible  in  the 
latter  case. 

According  to  Briicke's  theory  the  eyes  are  con- 
tinuously in  motion  and  the  observer  by  alternately 
increasing  or  decreasing  the  convergence  of  the  axes 
of  the  eyes,  combines  successively  the  different  parts 
of  the  two  scenes  as  seen  by  the  two  eyes  and  by 
running  the  point  of  sight  back  and  forth  by  trial  obtains 
a  distinct  perception  of  binocular  perspective  or  relief 
or  depth  of  space.  It  may  be  assumed  that  experience 
has  made  the  observer  proficient  in  this  appraisal 
which  he  arrives  at  almost  unconsciously,  although 
it  may  be  just  as  easy  to  accept  Wheatstone's  explan%n 
tion.  In  fact,  some  experiences  with  the  stereoscope 
appear  to  support  the  latter  theory. 

Wheatstone  discovered  that  the  dissimilar  pictures 


38  VISUAL  ILLUSIONS 

of  an  object  or  scene,  when  united  by  means  of  optical 
systems,  produce  a  visual  effect  similar  to  that  pro- 
duced by  the  actual  solid  object  or  scene  provided 
the  dissimilarity  is  the  same  as  that  between  two 
retinal  images  of  the  solid  object  or  scene.  This  is 
the  principle  upon  which  the  familiar  stereoscope  is 
founded.  Wheatstone  formulated  a  theory  which  may 
be  briefly  stated  as  follows :  In  viewing  a  solid  object 
or  a  scene  two  slightly  dissimilar  retinal  images  are 
formed  in  the  two  eyes  respectively,  but  the  mind  com- 
pletely fuses  them  into  one  "  mental  "  image.  When 
this  mental  fusion  of  the  two  really  dissimilar  retinal 
images  is  complete  in  this  way,  it  is  obvious  that  there 
cannot  exist  a  mathematical  coincidence.  The  re- 
sult is  a  perception  of  depth  of  space,  of  solidity,  of 
relief.  In  fact  the  third  dimension  is  perceived.  A 
stereoscope  accomplishes  this  in  essentially  the  same 
manner,  for  two  pictures,  taken  from  two  different 
positions  respectively  corresponding  to  the  positions 
of  the  eyes,  are  combined  by  means  of  optical  systems 
into  one  image. 

Lack  of  correct  size  and  position  of  the  individual 
elements  of  stereoscopic  pictures  are  easily  detected 
on  combining  them.  That  is,  their  dissimilarity  must 
exactly  correspond  to  that  between  two  views  of  an 
object  or  scene  from  the  positions  of  the  two  eyes 
respectively  (Fig.  2).  This  fact  has  been  made  use 
of  in  detecting  counterfeit  notes.  If  two  notes  made 
from  the  same  plate  are  viewed  in  a  stereoscope  and 
the  identical  figures  are  combined,  the  combination 
is  perfect  and  the  plane  of  the  combined  images  is 
perfectly  flat.  If  the  notes  are  not  made  from  the 


VISION  39 


same  plate  but  one  of  them  is  counterfeit,  slight 
variations  in  the  latter  are  unavoidable.  Such  varia- 
tions will  show  themselves  in  a  wavy  surface. 

The  unwillingness  of  the  visual  sense  to  combine 
the  two  retinal  images,  if  they  are  dissimilar  to  the 
extent  of  belonging  to  two  different  objects,  is  em- 
phasized by  means  of  colors.  For  example,  if  a  green 
glass  is  placed  over  one  eye  and  a  red  glass  over  the 
other,  the  colors  are  not  mixed  by  the  visual  sense. 
The  addition  of  these  two  colors  results  normally  in 
yellow,  with  little  or  no  suggestion  of  the  components — 
red  and  green.  But  in  the  foregoing  case  the  visual 
field  does  not  appear  of  a  uniform  yellow.  It  appears 
alternately  red  and  green,  as  though  the  colors 
were  rivaling  each  other  for  complete  mastery.  In 
fact,  this  phenomenon  has  been  termed  "  retinal 
rivalry." 

The  lenses  of  the  stereoscope  supplement  eye- 
lenses  and  project  on  the  retina  two  perfect  images 
of  a  near  object,  although  the  eyes  are  looking  at  a 
distant  object  and  are  therefore  not  accommodated 
for  the  near  one  (the  photographs).  The  lenses  en- 
large the  images  similar  to  the  action  of  a  perspective 
glass.  This  completes  the  illusion  of  an  object  or  of 
a  scene.  There  is  a  remarkable  distinctness  of  the 
perception  of  depth  of  space  and  therefore  a  wonder- 
ful resemblance  to  the  actual  object  or  scene.  It  is 
interesting  to  note  the  effect  of  taking  the  two  original 
photographs  from  distances  separated  by  several  feet. 
The  effect  is  apparently  to  magnify  depth.  It  is  note- 
worthy that  two  pictures  taken  from  an  airplane  at 
points  fifty  feet  or  so  apart,  when  combined  in  the 


40  VISUAL  ILLUSIONS 

stereoscope,  so  magnify  the  depth  that  certain  enemy- 
works  can  be  more  advantageously  detected  than  from 
ordinary  photographs. 

Stereoscopic  images  such  as  represented  in  Fig.  2 
may  be  combined  without  the  aid  of  the  stereoscope 
if  the  optical  axes  of  the  eye  can  be  sufficiently  con- 
verged or  diverged.  Such  images  or  pictures  are 
usually  upon  a  card  and  are  intended  to  be  combined 
beyond  the  plane  of  the  card,  for  it  is  in  this  position 
that  the  object  or  scene  can  be  perceived  in  natural 
perspective,  of  natural  size,  of  natural  form,  and  at 
natural  distance.  But  in  combining  them  the  eyes 
are  looking  at  a  distant  object  and  the  axes  are  parallel 
or  nearly  so.  Therefore,  the  eyes  are  focally  adjusted 
for  a  distant  object  but  the  light  comes  from  a  very 
near  object  —  the  pictures  on  the  card.  Myopic  eyes 
do  not  experience  this  difficulty  and  it  appears  that 
normal  vision  may  be  trained  to  overcome  it.  Normal 
eyes  are  aided  by  using  slightly  convex  lenses.  Such 
glasses  supplement  the  lenses  of  the  eye,  making 
possible  a  clear  vision  of  a  near  object  while  the  eyes 
are  really  looking  far  away  or,  in  other  words,  making 
possible  a  clear  image  of  a  near  object  upon  the  retina 
of  the  unadjusted  eye.  Stereoscopic  pictures  are 
usually  so  mounted  that  "  identical  points  "  on  the 
two  pictures  are  farther  apart  than  the  interocular 
distance  and  therefore  the  two  images  cannot  be 
combined  when  the  optical  axes  of  the  eyes  are  parallel 
or  nearly  so,  which  is  the  condition  when  looking  at 
a  distant  object.  In  such  a  case  the  two  pictures  must 
be  brought  closer  together. 

In  Figs.  2  and  3  are  found  "  dissimilar  "  drawings 


VISION  41 


of  the  correct  dissimilarity  of  stereoscopic  pictures. 
It  is  interesting  and  instructive  to  practice  combining 
these  with  the  unaided  eyes.  If  Fig.  2  is  held  at  an 
arm's  length  and  the  eyes  are  focused  upon  a  point 
several  inches  distant,  the  axes  will  be  sufficiently 


Fig.  2.  —  Stereoscopic  pictures  for  combining  by  converging 
or  diverging  the  optical  axes. 

converged  so  that  the  two  images  are  superposed.  It 
may  help  to  focus  the  eyes  upon  the  tip  of  a  finger 
until  the  stereoscopic  images  are  combined.  In  this 
case  of  converging  axes  the  final  combined  result  will 
be  the  appearance  of  a  hollow  tube  or  of  a  shell  of  a 
truncated  cone,  apparently  possessing  the  third  di- 
mension and  being  perceived  as  apparently  smaller 
than  the  actual  pictures  in  the  background  at  arm's 


Fig.  3.  —  Stereoscopic  pictures. 

length.  If  the  two  stereoscopic  pictures  are  combined 
by  looking  at  a  point  far  beyond  the  actual  position 
of  Fig.  2,  the  combined  effect  is  a  solid  truncated 
cone  but  perceived  as  of  about  the  same  size  and  at 
about  the  same  distance  from  the  eye  as  the  actual 


42  VISUAL  ILLUSIONS 

diagrams.  In  the  latter  case  the  smaller  end  of  the 
apparent  solid  appears  to  be  nearer  than  the  larger 
end,  but  in  the  former  case  the  reverse  is  true,  that  is, 
the  smaller  end  appears  to  be  at  a  greater  distance. 
The  same  experiments  may  be  performed  for  Fig.  3 
with  similar  results  excepting  that  this  appears  to  be 
a  shell  under  the  same  circumstances  that  Fig.  2 
appears  to  be  a  solid  and  vice  versa.  A  few  patient 
trials  should  be  rewarded  by  success,  and  if  so  the 
reader  can  gain  much  more  understanding  from  the 
actual  experiences  than  from  description. 

The  foregoing  discussion  of  vision  should  indicate 
the  complexity  of  the  visual  and  mental  activities  in- 
volved in  the  discrimination,  association,  and  inter- 
pretation of  the  data  obtained  through  the  eye.  The 
psychology  of  visual  perception  is  still  a  much  contro- 
verted domain  but  it  is  believed  that  the  glimpses  of 
the  process  of  vision  which  have  been  afforded  are 
sufficient  to  enable  the  reader  to  understand  many 
illusions  and  at  least  to  appreciate  more  fully  those 
whose  explanations  remain  in  doubt.  Certainly  these 
glimpses  and  a  knowledge  of  the  information  which 
visual  perception  actually  supplies  to  us  at  any  moment 
should  convince  us  that  the  visual  sense  has  acquired 
an  incomparable  facility  for  interpreting  the  objective 
world  for  us.  Clearness  of  vision  is  confined  to  a  small 
area  about  the  point  of  sight,  and  it  rapidly  diminishes 
away  from  this  point,  images  becoming  dim  and 
double.  We  sweep  this  point  of  sight  backward  and 
forward  and  over  an  extensive  field  of  view,  gathering 
all  the  distinct  impressions  into  one  mental  image. 
In  doing  this  the  unconscious  interpretation  of  the 


VISION  43 


muscular  activity  attending  accommodation  and  con- 
vergence of  the  eyes  aids  in  giving  to  this  mental 
picture  the  appearance  of  depth  by  establishing  relative 
distances  of  various  objects.  Certainly  the  acquired 
facility  is  remarkable. 


IV 

SOME  TYPES   OF   GEOMETRICAL 
ILLUSIONS 

NO  simple  classification  of  illusions  is  ample  or 
satisfactory,  for  there  are  many  factors  inter- 
woven. For  this  reason  no  claims  are  made 
for  the  various  divisions  of  the  subject  represented 
by  and  in  these  chapters  excepting  that  of  conven- 
ience. Obviously,  some  divisions  are  necessary  in 
order  that  the  variegated  subject  may  be  presentable. 
The  classification  used  appears  to  be  logical  but  very 
evidently  it  cannot  be  perfectly  so  when  the  "  logic  " 
is  not  wholly  available,  owing  to  the  disagreement 
found  among  the  explanations  offered  by  psycholo- 
gists. It  may  be  argued  that  the  "  geometrical " 
type  of  illusion  should  include  many  illusions  which 
are  discussed  in  other  chapters.  Indeed,  this  is  per- 
haps true.  However,  it  appears  to  suit  the  present 
purpose  to  introduce  this  phase  of  this  book  by  a  group 
of  illusions  which  involve  plane  geometrical  figures. 
If  some  of  the  latter  appear  in  other  chapters,  it  is 
because  they  seem  to  border  upon  or  to  include  other 
factors  beyond  those  apparently  involved  in  the  simple 
geometrical  type.  The  presentation  which  follows 
begins  (for  the  sake  of  clearness)  with  a  few  repre- 
sentative geometrical  illusions  of  various  types. 

The  Effect  of  the  Location  in  the  Visual  Field.— 
One  of  the  most  common  illusions  is  found  in  the 

44 


TYPES  OF  GEOMETRICAL  ILLUSIONS  45 

letter  "  S  "  or  figure  "  8."  Ordinarily  we  are  not 
strongly  conscious  of  a  difference  in  the  size  of  the 
upper  and  lower  parts  of  these  characters;  however, 
if  we  invert  them  (8888  SSSS)  the  difference  is  seen 
to  be  large.  The  question  arises,  Is  the  difference 
due  fundamentally  to  the  locations  of  the  two  parts 
in  the  visual  field?  It  scarcely  seems  credible  that 
visual  perception  innately  appraises  the  upper  part 
larger  than  the  lower,  or  the  lower  smaller  than  the 
upper  part  when  these  small  characters  are  seen  in 
thek  accustomed  position.  It  appears  to  be  possible 
that  here  we  have  examples  of  the  effect  of  learning 
or  experience  and  that  our  adaptive  visual  sense  has 
become  accustomed  to  overlook  the  actual  difference. 
That  is,  for  some  reason  through  being  confronted 
with  this  difference  so  many  times,  the  intellect  has 
become  adapted  to  it  and,  therefore,  has  grown  to 
ignore  it.  Regardless  of  the  explanation,  the  illusion 
exists  and  this  is  the  point  of  chief  interest.  For  the 
same  reason  the  curvature  of  the  retina  does  not 
appear  to  account  for  illusion  through  distortion  of 
the  image,  because  the  training  due  to  experience 
has  caused  greater  difficulties  than  this  to  disappear. 
We  must  not  overlook  the  tremendous  "  corrective  " 
influence  of  experience  upon  which  visual  perception 
for  the  adult  is  founded.  If  we  have  learned  to  "  cor- 
rect "  in  some  cases,  why  not  in  all  cases  which  we 
have  encountered  quite  generally? 

This  type  of  illusion  persists  in  geometrical  figures 
and  may  be  found  on  every  hand.  A  perfect  square 
when  viewed  vertically  appears  too  high,  although 
the  illusion  does  not  appear  to  exist  in  the  circle.  In 


46 


VISUAL  ILLUSIONS 


Fig.  4  the  vertical  line  appears  longer  than  the  hori- 
zontal line  of  the  same  length.  This  may  be  readily 
demonstrated  by  the  reader  by  medns  of  a  variety  of 
figures.  A  striking  case  is  found  in  Fig.  5,  where  the 
height  and  the  width  of  the  diagram  of  a  silk  hat  are 
equal.  Despite  the  actual  equality  the  height  appears 


Fig.  4.  —  The  vertical  line  appears  longer  than 
the  equal  horizontal  line  in  each  case. 

to  be  much  greater  than  the  width.  A  pole  or  a  tree 
is  generally  appraised  as  of  greater  length  when  it  is 
standing  than  when  it  lies  on  the  ground.  This  il- 
lusion may  be  demonstrated  by  placing  a  black  dot 
an  inch  or  so  above  another  on  a  white  paper.  Now, 
at  right  angles  to  the  original  dot  place  another  at  a 
horizontal  distance  which  appears  equal  to  the  vertical 
distance  of  the  first  dot  above  the  original.  On  turn- 
ing the  paper  through  ninety  degrees  or  by  actual 
measurement,  the  extent  of  the  illusion  will  become 
apparent.  By  doing  this  several  times,  using  various 
distances,  this  type  of  illusion  becomes  convincing. 


TYPES   OF  GEOMETRICAL  ILLUSIONS  47 

The  explanation  accepted  by  some  is  that  more 
effort  is  required  to  raise  the  eyes,  or  point  of  sight, 
through  a  certain  vertical  distance  than  through  an 
equal  horizontal  distance.  Perhaps  we  unconsciously 
appraise  effort  of  this  sort  in  terms  of  distance,  but 
is  it  not  logical  to  inquire  why  we  have  not  through 


Fig.  5.  —  The  vertical  dimension  is  equal  to  the  hori- 
zontal one,  but  the  former  appears  greater. 

experience  learned  to  sense  the  difference  between 
the  relation  of  effort  to  horizontal  distance  and  that 
of  effort  to  vertical  distance  through  which  the  point 
of  sight  is  moved?  We  are  doing  this  continuously, 
so  why  do  we  not  learn  to  distinguish;  furthermore, 
we  have  overcome  other  great  obstacles  in  developing 
our  visual  sense.  In  this  complex  field  of  physiological 
psychology  questions  are  not  only  annoying,  but  often 
disruptive. 


48  VISUAL  ILLUSIONS 

As  has  been  pointed  out  in  Chapter  II,  images  of 
objects  lying  near  the  periphery  of  the  visual  field  are 
more  or  less  distorted,  owing  to  the  structure  and  to 
certain  defects  of  parts  of  the  eye.  For  example,  a 
checkerboard  viewed  at  a  proper  distance  with  respect 
to  its  size  appears  quite  distorted  in  its  outer  regions. 
Cheap  cameras  are  likely  to  cause  similar  errors  in 
the  images  fixed  upon  the  photographic  plate.  Pho- 
tographs are  interesting  in  connection  with  visual  il- 
lusions, because  of  certain  distortions  and  of  the 
magnification  of  such  aspects  as  perspective.  In- 
cidentally in  looking  for  illusions,  difficulty  is  some- 
times experienced  in  seeing  them  when  the  actual 
physical  truths  are  known;  that  is,  in  distinguishing 
between  what  is  actually  seen  and  what  actually  exists. 
The  ability  to  make  this  separation  grows  with  prac- 
tice but  where  the  difficulty  is  obstinate,  it  is  well  for 
the  reader  to  try  observers  who  do  not  suspect  the 
truth. 

Illusions  of  Interrupted  Extent.  —  Distance  and 
area  appear  to  vary  in  extent,  depending  upon  whether 
they  are  filled  or  empty  or  are  only  partially  filled.' 
For  example,  a  series  of  dots  will  generally  appear 
longer  overall  than  an  equal  distance  between  two 
points.  This  may  be  easily  demonstrated  by  arrang- 
ing three  dots  in  a  straight  line  on  paper,  the  two  inter- 
vening spaces  being  of  equal  extent,  say  about  one 
or  two  inches  long.  If  in  one  of  the  spaces  a  series 
of  a  dozen  dots  is  placed,  this  space  will  appear  longer 
than  the  empty  space.  However,  if  only  one  dot  is 
placed  in  the  middle  of  one  of  the  empty  spaces,  this 
space  now  is  likely  to  appear  of  less  extent  than  the 


TYPES   OF  GEOMETRICAL  ILLUSIONS  49 

empty  space.  (See  Fig.  7.)  A  specific  example  of  this 
type  of  illusion  is  shown  in  Fig.  6.  The  filled  or  di- 
vided space  generally  appears  greater  than  the  empty 
or  undivided  space,  but  certain  qualifications  of  this 
statement  are  necessary.  In  a  the  divided  space 
unquestionably  appears  greater  than  the  empty  space. 
Apparently  the  filled  or  empty  space  is  more  important 


ii 


Fig.  6.  —  The  divided  or  filled  space  on  the  left  appears  longer  than  the  equal 

space  on  the  right. 

than  the  amount  of  light  which  is  received  from  the 
clear  spaces,  for  a  black  line  on  white  paper  appears 
longer  than  a  white  space  between  two  points  sep- 
arated a  distance  equal  to  the  length  of  the  black  line. 
Furthermore,  apparently  the  spacing  which  is  the 
most  obtrusive  is  most  influential  in  causing  the 
divided  space  to  appear  greater  for  a  than  for  b.  The 
illusion  still  persists  in  c. 

An  idea  of  the  magnitude  may  be  gained  from 
certain  experiments  by  Aubert.  He  used  a  figure 
similar  to  a  Fig.  6  containing  a  total  of  five  short  lines. 


60  VISUAL  ILLUSIONS 

Four  of  them  were  equally  spaced  over  a  distance 
of  100  mm.  corresponding  to  the  left  half  of  a,  Fig.  6. 
The  remaining  line  was  placed  at  the  extreme  right 
and  defined  the  limit  of  an  empty  space  also  100  mm. 
long.  In  all  cases,  the  length  of  the  empty  space  ap- 
peared about  ten  per  cent  less  than  that  of  the  space 

<L  b  c 

Fig.  7.  —  The  three  lines  are  of  equal  length. 

occupied  by  the  four  lines  equally  spaced.  Various 
experimenters  obtain  different  results,  and  it  seems 
reasonable  that  the  differences  may  be  accounted 
for,  partially  at  least,  by  different  degrees  of  uncon- 
scious correction  of  the  illusion.  This  emphasizes  the 
desirability  of  using  subjects  for  such  experiments 
who  have  no  knowledge  pertaining  to  the  illusion. 

As  already  stated  there  are  apparent  exceptions 
to  any  simple  rule,  for,  as  in  the  case  of  dots  cited  in  a 
preceding  paragraph,  the  illusion  depends  upon  the 

a    .      p      d 

Fig.  8.  —  The  distance  between  the  two  circles  on  the  left  is  equal  to  the 
distance  between  the  outside  edges  of  the  two  circles  on  the  right. 

manner  in  which  the  division  is  made.  For  example, 
in  Fig.  7,  a  and  c  are  as  likely  to  appear  shorter  than 
b  as  equal  to  it.  It  has  been  concluded  by  certain 
investigators  that  when  subdivision  of  a  line  causes 
it  to  appear  longer,  the  parts  into  which  it  is  divided 
or  some  of  them  are  likely  to  appear  shorter  than 
isolated  lines  of  the  same  length.  The  reverse  of 
this  statement  also  appears  to  hold.  For  example  in 


TYPES   OF  GEOMETRICAL  ILLUSIONS 


51 


Fig.  7,  a  appears  shorter  than 
b  and  the  central  part  appears 
lengthened,  although  the  total 
line  appears  shortened.  This 
illusion  is  intensified  by  leav- 
ing the  central  section  blank. 
A  figure  of  this  sort  can  be 
readily  drawn  by  the  reader 
by  using  short  straight  lines 
in  place  of  the  circles  in  Fig. 
8.  In  this  figure  the  space 
between  the  inside  edges  of 
the  two  circles  on  the  left  ap- 
pears larger  than  the  overall 
distance  between  the  outside 
edges  of  the  two  circles  on 
the  right,  despite  the  fact  that 
these  distances  are  equal.  It 
appears  that  mere  intensity  of 
retinal  stimulation  does  not 
account  for  these  illusions, 
but  rather  the  figures  which 
we  see. 

In  Fig.  9  the  three  squares 
are  equal  in  dimensions  but 
the  different  characters  of  the 
divisions  cause  them  to  ap- 
pear not  only  unequal,  but  no 
longer  squares.  In  Fig.  10 


Fig.  9.  —  Three  squares  of  equal  dimen- 
sions which  appear  different  in  area 
and  dimension. 


b 


52  VISUAL  ILLUSIONS 

the  distance  between  the  outside  edges  of  the  three 
circles  arranged  horizontally  appears  greater  than  the 
empty  space  between  the  upper  circle  and  the  left- 
hand  circle  of  the  group. 

Illusions  of  Contour. — The  illusions  of  this  type, 
or  exhibiting  this  influence,  are  quite  numerous.    In 


Fig.  10.  —  Tbe  vertical  distance  between  the  upper  circle  and  the  left-hand 
one  of  the  group  is  equal  to  the  overall  length  of  the  group  of  three  circles. 

Fig.  11  there  are  two  semicircles,  one  closed  by  a 
diameter,  the  other  unclosed.  The  latter  appears 
somewhat  flatter  and  of  slightly  greater  radius  than 
the  closed  one.  Similarly  in  Fig.  12  the  shorter  por- 
tion of  the  interrupted  circumference  of  a  circle  ap- 
pears flatter  and  of  greater  radius  of  curvature  than 
the  greater  portions.  In  Fig.  13  the  length  of  the 


TYPES   OF  GEOMETRICAL  ILLUSIONS 


53 


middle  space  and  of  the  open-sided  squares  are  equal. 
In  fact  there  are  two  uncompleted  squares  and  an 
empty  "  square  "  between,  the  three  of  which  are  of 
equal  dimensions.  However  the  middle  space  ap- 


Fig.  11.  —  Two  equal  semicircles.         Fig.  12.  —  Arcs  of  the  same  circle 

pears  slightly  too  high  and  narrow;  the  other  two 
appear  slightly  too  low  and  broad.  These  figures  are 
related  to  the  well-known  Muller-Lyer  illusion  il- 
lustrated in  Fig.  56.  Some  of  the  illusions  presented 
later  will  be  seen  to  involve  the  influence  of  contour. 


Fig.  13.  —  Three  incomplete  but  equal  squares. 

Examples  of  these  are  Figs.  55  and  60.  In  the  former, 
the  horizontal  base  line  appears  to  sag;  in  the  latter, 
the  areas  appear  unequal,  but  they  are  equal. 

Illusions  of  Contrast.  —  Those    illusions    due    to 
brightness  contrast  are  not  included  in  this  group, 


54 


VISUAL  ILLUSIONS 


for  "  contrast  "  here  refers  to  lines,  angles  and  areas 
of  different  sizes.  In  general,  parts  adjacent  to  large 
extents  appear  smaller  and  those  adjacent  to  small 
extents  appear  larger.  A  simple  case  is  shown  in 


Fig.  14.  —  Middle  sections  of  the  two  lines  are  equal. 

Fig.  14,  where  the  middle  sections  of  the  two  lines 
are  equal,  but  that  of  the  shorter  line  appears  longer 
than  that  of  the  longer  line.  In  Fig.  15  the  two  parts 
of  the  connecting  line  are  equal,  but  they  do  not  appear 
so.  This  illusion  is  not  as  positive  as  the  preceding 
one  and,  in  fact,  the  position  of  the  short  "vertical 
dividing  line  may  appear  to  fluctuate  considerably. 


Fig.  15.  —  An  effect  of  contrasting  areas  (Baldwin's  figure). 

Fig.  16  might  be  considered  to  be  an  illusion  of 
contour,  but  the  length  of  the  top  horizontal  line  of  the 
lower  figure  being  apparently  less  than  that  of  the  top 
line  of  the  upper  figure  is  due  largely  to  contrasting 
the  two  figures.  Incidentally,  it  is  difficult  to  believe 
that  the  maximum  horizontal  width  of  the  lower  figure 
is  as  great  as  the  maximum  height  of  the  figure.  At 
this  point  it  is  of  interest  to  refer  to  other  contrast 
illusions  such  as  Figs.  20,  57,  and  59. 


TYPES  OF  GEOMETRICAL  ILLUSIONS  55 

A  striking  illusion  of  contrast  is  shown  in  Fig.  17, 
where  the  central  circles  of  the  two  figures  are  equal, 
although  the  one  surrounded  by  the  large  circles  ap- 
pears much  smaller  than  the  other.  Similarly,  in 
Fig.  18  the  inner  circles  of  b  and  c  are  equal  but  that 
of  b  appears  the  larger.  The  inner  circle  of  a  appears 


Fig.  16.  —  An  illusion  of  contrast. 

larger  than  the  outer  circle  of  &,  despite  their  actual 
equality. 

In  Fig.  19  the  circle  nearer  the  apex  of  the  angle 
appears  larger  than  the  other.  This  has  been  pre- 
sented as  one  reason  why  the  sun  and  moon  appear 
larger  at  the  horizon  than  when  at  higher  altitudes. 
This  explanation  must  be  based  upon  the  assumption 
that  we  interpret  the  "  vault "  of  the  sky  to  meet 


56 


VISUAL  ILLUSIONS 


o 


o 


Fig.  17.  —  Equal  circles  which  appear  unequal  due  to  contrast 
(Ebbinghaus*  figure). 


Fig.  18.  —  Equal  circles  appearing  unequal  owing  to  contrasting 
concentric  circles. 


TYPES   OF  GEOMETRICAL  ILLUSIONS 


57 


at  the  horizon  in  a  manner  somewhat  similar  to  the 
angle  but  it  is  difficult  to  imagine  such  an  angle  made 
by  the  vault  of  the  sky  and  the  earth's  horizon.  If 


Fig.  19.  —  Circles  influenced  by  position  within  an  angle. 

there  were  one  in  reality,  it  would  not  be  seen  in 
profile. 

If  two  angles  of  equal  size  are  bounded  by  small 
and  large  angles  respectively,  the  apex  in  each  case 


Fig.  20.  —  Contrasting  angles. 

being  common  to  the  inner  and  two  bounding  angles, 
the  effect  of  contrast  is  very  apparent,  as  seen  in  Fig.  20. 
In  Fig.  57  are  found  examples  of  effects  of  lines  con- 
trasted as  to  length. 


58 


VISUAL  ILLUSIONS 


The  reader  may  readily  construct  an  extensive 
variety  of  illusions  of  contrast;  in  fact,  contrast  plays 
a  part  in  most  geometrical-optical  illusions.  The 


Fig.  21.  — Owing  to  perspective  the  right 
angles  appear  oblique  and  vice  versa. 

contrasts  may  be  between  existing  lines,  areas,  etc., 
or  the  imagination  may  supply  some  of  them. 

Illusions  of  Perspective.  —  As  the  complexity  of 
figures  is  increased  the  number  of  possible  illusions 

X 


Y 


Fig.  22.  —  Two  equal  diagonals  which  appear  unequal. 

is  multiplied.  In  perspective  we  have  the  influences 
of  various  factors  such  as  lines,  angles,  and  some- 
times contour  and  contrast.  In  Fig.  21  the  sug- 


TYPES  OF  GEOMETRICAL  ILLUSIONS  69 

gestion  due  to  the  perspective  of  the  cube  causes 
right  angles  to  appear  oblique  and  oblique  angles  to 
appear  to  be  right  angles.  This  figure  is  particularly 
illusive.  It  is  interesting  to  note  that  even  an  after- 
image of  a  right-angle  cross  when  projected  upon  a 
wall  drawn  in  perspective  in  a  painting  will  appear 
oblique. 


Fig.  23.  —  Apparent  variations  in  the  distance  between 
two  parallel  lines. 

A  striking  illusion  involving  perspective,  or  at  least 
the  influence  of  angles,  is  shown  in  Fig.  22.  Here  the 
diagonals  of  the  two  parallelograms  are  of  equal 
length  but  the  one  on  the  right  appears  much  smaller. 
That  AX  is  equal  in  length  to  A  Y  is  readily  demon- 
strated by  describing  a  circle  from  the  center  A  and 
with  a  radius  equal  to  AX.  It  will  be  found  to  pass 
through  the  point  Y.  Obviously,  geometry  abounds 
in  geometrical-optical  illusions. 


60 


VISUAL  ILLUSIONS 


The  effect  of  contrast  is  seen  in  a  in  Fig.  23 ;  that 
is,  the  short  parallel  lines  appear  further  apart  than 
the  pair  of  long  ones.  By  adding  the  oblique  lines 
at  the  ends  of  the  lower  pair  in  &,  these  parallel  lines 


Fig.  24.  —  A  striking  illusion  of  perspective. 

» 

now  appear  further  apart  than  the  horizontal  parallel 
lines  of  the  small  rectangle. 

The  influence  of  perspective  is  particularly  ap- 
parent in  Fig.  24,  where  natural  perspective  lines 
are  drawn  to  suggest  a  scene.  The  square  columns 
are  of  the  same  size  but  the  farther  one,  for  example, 
being  apparently  the  most  distant  and  of  the  same 


TYPES  OF  GEOMETRICAL  ILLUSIONS 


61 


physical  dimensions,  actually  appears  much  larger. 
Here  is  a  case  where  experience,  allowing  for  a  di- 
minution of  size  with  increasing  distance,  actually 
causes  the  column  on  the  right  to  appear  larger  than 
it  really  is.  The  artist  will  find  this  illusion  even  more 


Fig.  25.  —  Distortion  of  a  square  due  to  superposed  lines. 

striking  if  he  draws  three  human  figures  of  the  same 
size  but  similarly  disposed  in  respect  to  perspective 
lines.  Apparently  converging  lines  influence  these 
equal  figures  in  proportion  as  they  suggest  perspective. 
Although  they  are  not  necessarily  illusions  of 
perspective,  Figs.  25  and  26  are  presented  here  be- 
cause they  involve  similar  influences.  In  Fig.  25  the 
hollow  square  is  superposed  upon  groups  of  oblique 
lines  so  arranged  as  to  apparently  distort  the  square. 


62  VISUAL  ILLUSIONS 

In  Fig.  26  distortions  of  the  circumference  of  a  circle 
are  obtained  in  a  similar  manner. 

It  is  interesting  to  note  that  we  are  not  particu- 
larly conscious  of  perspective,  but  it  is  seen  that  it 


Fig.  26.  —  Distortion  of  a  circle  due  to  superposed  lines. 

has  been  a  factor  in  the  development  of  our  visual 
perception.  In  proof  of  this  we  might  recall  the  first 
time  as  children  we  were  asked  to  draw  a  railroad 
track  trailing  off  in  the  distance.  Doubtless,  most 
of  us  drew  two  parallel  lines  instead  of  converging  ones. 


TYPES  OF  GEOMETRICAL  ILLUSIONS  63 

A  person  approaching  us  is  not  sensibly  perceived 
to  grow.  He  is  more  likely  to  be  perceived  all  the  time 
as  of  normal  size.  The  finger  held  at  some  distance 
may  more  than  cover  the  object  such  as  a  distant 
person,  but  the  finger  is  not  ordinarily  perceived 
as  larger  than  the  person.  Of  course,  when  we  think 
of  it  we  are  conscious  of  perspective  and  of  the  in- 
crease in  size  of  an  approaching  object.  When  a 
locomotive  or  automobile  approaches  very  rapidly, 
this  "  growth  "  is  likely  to  be  so  striking  as  to  be 
generally  noticeable.  The  reader  may  find  it  of 
interest  at  this  point  to  turn  to  illustrations  in  other 
chapters. 

The  foregoing  are  a  few  geometrical  illusions  of 
representative  types.  These  are  not  all  the  types  of 
illusions  by  any  means  and  they  are  only  a  few  of  an 
almost  numberless  host.  These  have  been  presented 
in  a  brief  classification  in  order  that  the  reader  might 
not  be  overwhelmed  by  the  apparent  chaos.  Various 
special  and  miscellaneous  geometrical  illusions  are 
presented  in  later  chapters. 


EQUIVOCAL  FIGURES 

MANY  figures  apparently  change  in  appearance 
owing  to  fluctuations  in  attention  and  in  as- 
sociations. A  human  profile  in  intaglio  (Figs. 
72  and  73)  may  appear  as  a  bas-relief.  Crease  a  card 
in  the  middle  to  form  an  angle  and  hold  it  at  an  arm's 
length.  When  viewed  with  one  eye  it  can  be  made 
to  appear  open  in  one  way  or  the  other;  that  is,  the 
angle  may  be  made  to  appear  pointing  toward  the 
observer  or  away  from  him.  The  more  distant  part 
of  an  object  may  be  made  to  appear  nearer  than  the 
remaining  part.  Plane  diagrams  may  seem  to  be 
solids.  Deception  of  this  character  is  quite  easy  if  the 
light-source  and  other  extraneous  factors  are  con- 
cealed from  the  observer.  It  is  very  interesting  to 
study  these  fluctuating  figures  and  to  note  the  various 
extraneous  data  which  lead  us  to  judge  correctly. 
Furthermore,  it  becomes  obvious  that  often  we  see 
what  we  expect  to  see.  For  example,  we  more  com- 
monly encounter  relief  than  intaglio;  therefore,  we 
are  likely  to  think  that  we  are  looking  at  the  former. 
Proper  consideration  of  the  position  of  the  domi- 
nant light-source  and  of  the  shadows  will  usually 
provide  the  data  for  a  correct  conclusion.  However, 
habit  and  probability  are  factors  whose  influence  is 
difficult  to  overcome.  Our  perception  is  strongly 

^_— ~ -64 


EQUIVOCAL  FIGURES  65 

associated  with  accustomed  ways  of  seeing  objects 
and  when  the  object  is  once  suggested  it  grasps  our 
mind  completely  in  its  stereotyped  form.  Stairs, 
glasses,  rings,  cubes,  and  intaglios  are  among  the 
objects  commonly  used  to  illustrate  this  type  of  il- 
lusion. In  connection  with  this  type,  it  is  well  to 


Fig.  27.  —  Illustrating  fluctuation  of  attention. 

realize  how  tenaciously  we  cling  to  our  perception 
of  the  real  shapes  of  objects.  For  example,  a  cube 
thrown  into  the  air  in  such  a  manner  that  it  presents 
many  aspects  toward  us  is  throughout  its  course 
a  cube. 

The  figures  which  exhibit  these  illusions  are 
obviously  those  which  are  capable  of  two  or  more 
spatial  relations.  The  double  interpretation  is  more 
readily  accomplished  by  monocular  than  by  binocular 
vision.  Fig.  27  consists  of  identical  patterns  in  black 
and  white.  By  gazing  upon  this  steadily  it  will  appear 


66  VISUAL  ILLUSIONS 


to  fluctuate  in  appearance  from  a  white  pattern  upon 
a  black  background  to  a  black  pattern  upon  a  white 
background.  Sometimes  fluctuation  of  attention  ap- 
parently accounts  for  the  change  and,  in  fact,  this  can 
be  tested  by  willfully  altering  the  attention  from  a 
white  pattern  to  a  black  one.  Incidentally  one  in- 


Fig.  28.  —  The  grouping  of  the  circles  fluctuates. 

vestigator  found  that  the  maximum  rate  of  fluctuation 
was  approximately  equal  to  the  pulse  rate,  although 
no  connection  between  the  two  was  claimed.  It  has 
also  been  found  that  inversion  is  accompanied  by 
a  change  in  refraction  of  the  eye. 

Another  example  is  shown  in  Fig.  28.  This  may 
appear  to  be  white  circles  upon  a  black  background 
or  a  black  mesh  upon  a  white  background.  However, 
the  more  striking  phenomenon  is  the  change  in  the 
grouping  of  the  circles  as  attention  fluctuates.  We 
may  be  conscious  of  hollow  diamonds  of  circles,  one 
inside  the  other,  and  then  suddenly  the  pattern  may 
change  to  groups  of  diamonds  consisting  of  four 


EQUIVOCAL  FIGURES  67 

circles  each.  Perhaps  we  may  be  momentarily  con- 
scious of  individual  circles;  then  the  pattern  may 
change  to  a  hexagonal  one,  each  "hexagon"  con- 
sisting of  seven  circles  —  six  surrounding  a  central 
one.  The  pattern  also  changes  into  parallel  strings 
of  circles,  triangles,  etc. 


Fig.  29.  —  Crossed  lines  which  may  be  interpreted  in  two  ways. 

The  crossed  lines  in  Fig.  29  can  be  seen  as  right 
angles  in  perspective  with  two  different  spatial  ar- 
rangements of  one  or  both  lines.  In  fact  there  is 
quite  a  tendency  to  see  such  crossed  lines  as  right 
angles  in  perspective.  The  two  groups  on  the  right 
represent  a  simplified  Zollner's  illusion  (Fig.  37). 
The  reader  may  find  it  interesting  to  spend  some 
time  viewing  these  figures  and  in  exercising  his  ability 
to  fluctuate  his  attention.  In  fact,  he  must  call  upon 
his  imagination  in  these  cases.  Sometimes  the 


68  VISUAL  ILLUSIONS 

changes  are  rapid  and  easy  to  bring  about.  At  other 
moments  he  will  encounter  an  aggravating  stubborn- 
ness. Occasionally  there  may  appear  a  conflict  of 
two  appearances  simultaneously  in  the  same  figure. 
The  latter  may  be  observed  occasionally  in  Fig.  30. 


Fig.  30.  —  Reversible'cubes. 

Eye-movements  are  brought  forward  by  some  to  aid 
in  explaining  the  changes. 

In  Fig.  30  a  reversal  of  the  aspect  of  the  individual 
cubes  or  of  their  perspective  is  very  apparent.  At 
rare  moments  the  effect  of  perspective  may  be  com- 
pletely vanquished  and  the  figure  be  made  to  appear 
as  a  plane  crossed  by  strings  of  white  diamonds  and 
zigzag  black  strips. 


EQUIVOCAL  FIGURES  69 

The  illusion  of  the  bent  card  or  partially  open 
book  is  seen  in  Fig.  31.  The  tetrahedron  in  Fig.  32 
may  appear  either  as  erect  on  its  base  or  as  leaning 
backward  with  its  base  seen  from  underneath. 

The  series  of  rings  in  Fig.  33  may  be  imagined 


Fig.  31.  —  The  reversible  "  open         Fig.  32.  —  A  reversible  tetrahedron, 
book  "  (after  Mach). 

to  form  a  tube  such  as  a  sheet-metal  pipe  with  its 
axis  lying  in  either  of  two  directions.  Sometimes  by 
closing  one  eye  the  two  changes  in  this  type  of  il- 
lusion are  more  readily  brought  about.  It  is  also 
interesting  to  close  and  open  each  eye  alternately, 
at  the  same  time  trying  to  note  just  where  the  at- 
tention is  fixed. 

The  familiar  staircase  is  represented  in  Fig.  34. 
It  is  likely  to  appear  in  its  usual  position  and  then 


70  VISUAL  ILLUSIONS 

suddenly  to  invert.  It  may  aid  in  bringing  about  the 
reversal  to  insist  that  one  end  of  a  step  is  first  nearer 
than  the  other  and  then  farther  away.  By  focusing 


Fig.  33.  —  Reversible  perspective  of  a 
group  of  rings  or  of  a  tube. 

the  attention  in  this  manner  the  fluctuation  becomes 
an  easy  matter  to  obtain. 

In  Fig.  35  is  a  similar  example.    First  one  part 


Fig.  34.  —  Schroder's  reversible  staircase. 

will  appear  solid  and  the  other  an  empty  corner,  then 
suddenly  both  are  reversed.  However,  it  is  striking 
to  note  one  half  changes  while  the  other  remains  un- 


EQUIVOCAL  FIGURES 


71 


changed,  thus  producing  momentarily  a  rather  peculiar 
figure  consisting  of  two  solids,  for  example,  attached 
by  necessarily  warped  surfaces. 

Perhaps  the  reader  has  often  witnessed  the  striking 
illusion  of  some  portraits  which  were  made  of  sub- 


Fig.  35.  —  Thiery's  figure. 

jects  looking  directly  at  the  camera  or  painter.  Re- 
gardless of  the  position  of  the  observer  the  eyes  of 
the  portrait  appear  to  be  directed  toward  him.  In 
fact,  as  the  observer  moves,  the  eyes  in  the  picture 
follow  him  so  relentlessly  as  to  provoke  even  a  feeling 
of  uncanniness.  This  fact  is  accounted  for  by  the 
absence  of  a  third  dimension,  for  a  sculptured  model 
of  a  head  does  not  exhibit  this  feature.  Perspective 
plays  a  part  in  some  manner,  but  no  attempt  toward 
explanation  will  be  made. 


72  VISUAL  ILLUSIONS 

In  Fig.  36  are  two  sketches  of  a  face.  One  ap- 
pears to  be  looking  at  the  observer,  but  the  other  does 
not.  If  the  reader  will  cover  the  lower  parts  of  the 
two  figures,  leaving  only  the  two  pairs  of  eyes  show- 
ing, both  pairs  will  eventually  appear  to  be  looking  at 
the  observer.  Perhaps  the  reader  will  be  conscious 
of  mental  effort  and  the  lapse  of  a  few  moments 
before  the  eyes  on  the  left  are  made  to  appear  to  be 
looking  directly  at  him.  Although  it  is  not  claimed 
that  this  illusion  is  caused  by  the  same  conditions  as 
those  immediately  preceding,  it  involves  attention. 
At  least,  it  is  fluctuating  in  appearance  and  therefore 
is  equivocal.  It  is  interesting  to  note  the  influence 
of  the  other  features  (below  the  eyes).  The  per- 
spective of  these  is  a  powerful  influence  in  "  directing  " 
the  eyes  of  the  sketch. 

In  the  foregoing  only  definite  illusions  have  been 
presented  which  are  universally  witnessed  by  normal 
persons.  There  are  no  hallucinatory  phases  in  the 
conditions  or  causes.  It  is  difficult  to  divide  these 
with  definiteness  from  certain  illusions  of  depth  as 
discussed  in  Chapter  VII.  The  latter  undoubtedly  are 
sometimes  entwined  to  some  extent  with  hallucina- 
tory phases;  in  fact,  it  is  doubtful  if  they  are  not 
always  hallucinations  to  some  degree.  Hallucinations 
are  not  of  interest  from  the  viewpoint  of  this  book, 
but  illusions  of  depth  are  treated  because  they  are  of 
interest.  They  are  either  hallucinations  or  are  on 
the  border-line  between  hallucinations  and  those 
illusions  which  are  almost  universally  experienced  by 
normal  persons  under  similar  conditions.  The  latter 
statement  does  not  hold  for  illusions  of  depth  in 


EQUIVOCAL  FIGURES 


73 


74  VISUAL  ILLUSIONS 

which  objects  may  be  seen  alternately  near  and  far, 
large  and  small,  etc.,  although  they  are  not  neces- 
sarily pure  hallucinations  as  distinguished  from  the 
types  of  illusions  regarding  which  there  is  general 
perceptual  agreement. 

In  explanation  of  the  illusory  phenomena  pertain- 
ing to  such  geometrical  figures  as  are  discussed  in  the 
foregoing  paragraphs,  chiefly  two  different  kinds  of 
hypotheses  have  been  offered.  They  are  respectively 
psychological  and  physiological,  although  there  is  more 
or  less  of  a  mixture  of  the  two  in  most  attempts  toward 
explanation.  The  psychological  hypotheses  introduce 
such  factors  as  attention,  imagination,  judgment,  and 
will.  Hering  and  also  Helmholtz  claim  that  the  kind 
of  inversion  which  occurs  is  largely  a  matter  of  chance 
or  of  volition.  The  latter  holds  that  the  perception  of 
perspective  figures  is  influenced  by  imagination  or  the 
images  of  memory.  That  is,  if  one  form  of  the  figure 
is  vividly  imagined  the  perception  of  it  is  imminent. 
Helmholtz  has  stated  that,  "Glancing  at  a  figure  we 
observe  spontaneously  one  or  the  other  form  of  per- 
spective and  usually  the  one  that  is  associated  in  our 
memory  with  the  greatest  number  of  images." 

The  physiological  hypotheses  depend  largely  upon 
such  factors  as  accommodation  and  eye-movement. 
Necker  held  to  the  former  as  the  chief  cause.  He 
has  stated  that  the  part  of  the  figure  whose  image  lies 
near  the  fovea  is  estimated  as  nearer  than  those 
portions  in  the  peripheral  regions  of  the  visual  field. 
This  hypothesis  is  open  to  serious  objections.  Wundt 
contends  that  the  inversion  is  caused  by  changes  in 
the  points  and  lines  of  fixation.  He  says,  "  The  image 


EQUIVOCAL  FIGURES  75 

of  the  retina  ought  to  have  a  determined  position  if  a 
perspective  illusion  is  to  appear;  but  the  form  of  this 
illusion  is  entirely  dependent  on  motion  and  direction." 
Some  hypotheses  interweave  the  known  facts  of  the 
nervous  system  with  psychological  facts  but  some  of 
these  are  examples  of  a  common  anomaly  in  theori- 
zation,  for  facts  plus  facts  do  not  necessarily  result  in  a 
correct  theory.  That  is,  two  sets  of  facts  interwoven 
do  not  necessarily  yield  an  explanation  which  is 
correct. 


VI 
THE  INFLUENCE  OF  ANGLES 

AS  previously  stated,  no  satisfactory  classification 
of  visual  illusions  exists,  but  in  order  to  cover 
the  subject,  divisions  are  necessary.  For  this 
reason  the  reader  is  introduced  in  this  chapter  to  the 
effects  attending  the  presence  of  angles.  By  no 
means  does  it  follow  that  this  group  represents  an- 
other type,  for  it  really  includes  many  illusions  of 
several  types.  The  reason  for  this  grouping  is  that 
angles  play  an  important  part,  directly  or  indirectly,  in 
the  production  of  illusions.  For  a  long  time  many 
geometrical  illusions  were  accounted  for  by  "  over- 
estimation  "  or  "  underestimation "  of  angles,  but 
this  view  has  often  been  found  to  be  inadequate. 
However,  it  cannot  be  denied  that  many  illusions  are 
due  at  least  to  the  presence  of  angles. 

Apparently  Zollner  was  the  first  to  describe  an 
illusion  which  is  illustrated  in  simple  form  in  Fig.  29 
and  more  elaborately  in  Figs.  37  to  40.  The  two 
figures  at  the  right  of  Fig.  29  were  drawn  for  another 
purpose  and  are  not  designed  favorably  for  the  effect, 
although  it  may  be  detected  when  the  figure  is  held 
at  a  distance.  Zollner  accidentally  noticed  the  il- 
lusion on  a  pattern  designed  for  a  print  for  dress- 
goods.  The  illusion  is  but  slightly  noticeable  in 
Fig.  29,  but  by  multiplying  the  number  of  lines  (and 
angles)  the  long  parallel  lines  appear  to  diverge  in 

76 


THE  INFLUENCE   OF  ANGLES 


77 


the  direction  that  the  crossing  lines  converge.  Zollner 
studied  the  case  thoroughly  and  established  various 
facts.  He  found  that  the  illusion  is  greatest  when  the 
long  parallel  lines  are  inclined  about  45  degrees  to 
the  horizontal.  This  may  be  accomplished  for  Fig.  37, 
by  turning  the  page  (held  in  a  vertical  plane)  through 


Fig.  37.  —  Zollner's  illusion  of  direction. 

an  angle  of  45  degrees  from  normal.  The  illusion 
vanishes  when  held  too  far  from  the  eye  to  distinguish 
the  short  crossing  lines,  and  its  strength  varies  with 
the  inclination  of  the  oblique  lines  to  the  main  parallels. 
The  most  effective  angle  between  the  short  crossing 
lines  and  the  main  parallels  appears  to  be  approxi- 
mately 30  degrees.  In  Fig.  37  there  are  two  illusions 
of  direction.  The  parallel  vertical  strips  appear  un- 
parallel  and  the  right  and  left  portions  of  the  oblique 
cross-lines  appear  to  be  shifted  vertically.  It  is 
interesting  to  note  that  steady  fixation  diminishes  and 
even  destroys  the  illusion. 


78  VISUAL  ILLUSIONS 

The  maximum  effectiveness  of  the  illusion,  when 
the  figure  is  held  so  that  the  main  parallel  lines  are 
at  an  inclination  of  about  45  degrees  to  the  horizontal 
was  accounted  for  by  Zollner  as  the  result  of  less 
visual  experience  in  oblique  directions.  He  insisted 
that  it  takes  less  time  and  is  easier  to  infer  divergence 
or  convergence  than  parallelism.  This  explanation  ap- 
pears to  be  disproved  by  a  figure  in  which  slightly 
divergent  lines  are  used  instead  of  parallel  ones. 
Owing  to  the  effect  of  the  oblique  crossing  lines,  the 
diverging  lines  may  be  made  to  appear  parallel. 
Furthermore  it  is  difficult  to  attach  much  importance 
to  Zollner's  explanation  because  the  illusion  is  visible 
under  the  extremely  brief  illumination  provided  by 
one  electric  spark.  Of  course,  the  duration  of  the 
physiological  reaction  is  doubtless  greater  than  that 
of  the  spark,  but  at  best  the  time  is  very  short.  Hering 
explained  the  Zollner  illusion  as  due  to  the  curvature 
of  the  retina,  and  the  resulting  difference  in  the 
retinal  images,  and  held  that  acute  angles  appear 
relatively  too  large  and  obtuse  ones  too  small.  The 
latter  has  been  found  to  have  limitations  in  the  ex- 
planation of  certain  illusions. 

This  Zollner  illusion  is  very  striking  and  may  be 
constructed  in  a  variety  of  forms.  In  Fig.  37  the 
effect  is  quite  apparent  and  it  is  interesting  to  view 
the  figure  at  various  angles.  For  example,  hold  the 
figure  so  that  the  broad  parallel  lines  are  vertical. 
The  illusion  is  very  pronounced  in  this  position; 
however,  on  tilting  the  page  backward  the  illusion 
finally  disappears.  In  Fig.  38  the  short  oblique  lines 
do  not  cross  the  long  parallel  lines  and  to  make  the 


THE  INFLUENCE  OF  ANGLES  79 


Fig.  38.  —  Parallel  lines  which  do  not  appear  so. 


Fig.  39.  —  Wundt's  illusion  of  direction. 


80  VISUAL  ILLUSIONS 

illusion  more  striking,  the  obliquity  of  the  short  lines 
is  reversed  at  the  middle  of  the  long  parallel  lines. 
Variations  of  this  figure  are  presented  in  Figs.  39  and 
40.  In  this  case  by  steady  fixation  the  perspective 
effect  is  increased  but  there  is  a  tendency  for  the 
parallel  lines  to  appear  more  nearly  truly  parallel 


Fig.  40.  —  Bering's  illusion  of  direction. 

than  when  the  point  of  sight  is  permitted  to  roam  over 
the  figures. 

Many  investigations  of  the  Zollner  illusion  are 
recorded  in  the  literature.  From  these  it  is  obvious 
that  the  result  is  due  to  the  additive  effects  of  many 
simple  illusions  of  angle.  In  order  to  give  an  idea 
of  the  manner  in  which  such  an  illusion  may  be  built 
up  the  reasoning  of  Jastrow  1  will  be  presented  in 
condensed  form.  When  two  straight  lines  such  as 
A  and  B  in  Fig.  41  are  separated  by  a  space  it  is  usu- 
ally possible  to  connect  the  two  mentally  and  to  de- 
termine whether  or  not,  if  connected,  they  would  lie 


THE  INFLUENCE  OF  ANGLES  81 

on  a  straight  line.  However,  if  another  line  is  con- 
nected to  one,  thus  forming  an  angle  as  C  does  with 
Ay  the  lines  which  appeared  to  be  continuous  (as  A 
and  B  originally)  no  longer  appear  so.  The  converse 
is  also  true,  for  lines  which  are  not  in  the  same  straight 
line  may  be  made  to  appear  to  be  by  the  addition  of 
another  line  forming  a  proper  angle.  All  these  vari- 


B 


Fig.  41.  —  Simple  effect  of  angles. 

ations  cannot  be  shown  in  a  single  figure,  but  the  reader 
will  find  it  interesting  to  draw  them.  Furthermore, 
the  letters  used  on  the  diagram  in  order  to  make  the 
description  clearer  may  be  confusing  and  these  can  be 
eliminated  by  redrawing  the  figure.  In  Fig.  41  the 
obtuse  angle  AC  tends  to  tilt  A  downward,  so  ap- 
parently if  A  were  prolonged  it  would  fall  below  B. 
Similarly,  C  appears  to  fall  to  the  right  of  D. 

This  illusion  apparently  is  due  to  the  presence  of 


82  VISUAL  ILLUSIONS 

the  angle  and  the  effect  is  produced  by  the  presence 
of  right  and  acute  angles  to  a  less  degree.  The  il- 
lusion decreases  or  increases  in  general  as  the  angle 
decreases  or  increases  respectively. 

Although  it  is  not  safe  to  present  simple  state- 
ments in  a  field  so  complex  as  that  of  visual  illusion 
where  explanations  are  still  controversial,  it  is  perhaps 
possible  to  generalize  as  Jastrow  did  in  the  foregoing 
case  as  follows:  If  the  direction  of  an  angle  is  that 
of  the  line  bisecting  it  and  pointing  toward  the  apex, 
the  direction  of  the  sides  of  an  angle  will  apparently 
be  deviated  toward  the  direction  of  the  angle.  The 
deviation  apparently  is  greater  with  obtuse  than  with 
acute  angles,  and  when  obtuse  and  acute  angles  are 
so  placed  in  a  figure  as  to  give  rise  to  opposite  devi- 
ations, the  greater  angle  will  be  the  dominant  in- 
fluence. 

Although  the  illusion  in  such  simple  cases  as 
Fig.  41  is  slight,  it  is  quite  noticeable.  The  effect  of 
the  addition  of  many  of  these  slight  individual  in- 
fluences is  obvious  in  accompanying  figures  of  greater 
complexity.  These  individual  effects  can  be  so  multi- 
plied and  combined  that  many  illusory  figures  may 
be  devised. 

In  Fig.  42  the  oblique  lines  are  added  to  both 
horizontal  lines  in  such  a  manner  that  A  is  tilted 
downward  at  the  angle  and  B  is  tilted  upward  at  the 
angle  (the  letters  corresponding  to  similar  lines  in 
Fig.  41).  In  this  manner  they  appear  to  be  deviated 
considerably  out  of  their  true  straight  line.  If  the 
reader  will  draw  a  straight  line  nearly  parallel  to  D 
in  Fig.  41.  and  to  the  right,  he  will  find  it  helpful. 


THE  INFLUENCE  OF  ANGLES  83 

This  line  should  be  drawn  to  appear  to  be  a  continu- 
ation of  C  when  the  page  is  held  so  D  is  approxi- 
mately horizontal.  This  is  a  simple  and  effective 
means  of  testing  the  magnitude  of  the  illusion,  for  it 


Fig.  42.    The  effect  of  two  angles  in  tilting  the  horizontal  lines. 

is  measured  by  the  degree  of  apparent  deviation 
between  D  and  the  line  drawn  adjacent  to  it,  which 
the  eye  will  tolerate.  Another  method  of  obtaining 
such  a  measurement  is  to  begin  with  only  the  angle 
and  to  draw  the  apparent  continuation  of  one  of  its 

D 


Fig.  43.    The  effect  of  crossed  lines  upon  their  respective  apparent 

directions. 

lines  with  a  space  intervening.  This  deviation  from 
the  true  continuation  may  then  be  readily  deter- 
mined. 

A  more  complex  case  is  found  in  Fig.  43  where  the 
effect  of  an  obtuse  angle  ACD  is  to  make  the  continu- 


84  VISUAL  ILLUSIONS 

ation  of  AB  apparently  fall  below  FG  and  the  effect 
of  the  acute  angle  is  the  reverse.  However,  the  net 
result  is  that  due  to  the  preponderance  of  the  effect 
of  the  larger  angle  over  that  of  the  smaller.  The  line 
EC  adds  nothing,  for  it  merely  introduces  two  angles 
which  reinforce  those  above  AB.  The  line  BC  may 
be  omitted  or  covered  without  appreciably  affecting 
the  illusion. 

In  Fig.  44  two  obtuse  angles  are  arranged  so  that 
their  effects  are  additive,  with  the  result  that  the 


Fig.  44.  —  Another  step  toward  the  Zollner  illusion. 

horizontal  lines  apparently  deviate  maximally  for  such 
a  simple  case.  Thus  it  is  seen  that  the  tendency  of 
the  sides  of  an  angle  to  be  apparently  deviated  toward 
the  direction  of  the  angle  may  result  in  an  apparent 
divergence  from  parallelism  as  well  as  in  making 
continuous  lines  appear  discontinuous.  The  illusion 
in  Fig.  44  may  be  strengthened  by  adding  more  lines 
parallel  to  the  oblique  lines.  This  is  demonstrated 
in  Fig.  38  and  in  other  illustrations.  In  this  manner 
striking  illusions  are  built  up. 

If  oblique  lines  are  extended  across  vertical  ones, 
as  in  Figs.  45  and  46,  the  illusion  is  seen  to  be  very 
striking.  In  Fig.  45  the  oblique  line  on  the  right  if 


THE  INFLUENCE  OF  ANGLES 


85 


extended  would  meet  the  upper  end  of  the  oblique 
line  on  the  left ;  however,  the  apparent  point  of  inter- 
section is  somewhat  lower  than  it  is  in  reality.  In 
Fig.  46  the  oblique  line  on  the  left  is  in  the  same 
straight  line  with  the  lower  oblique  line  on  the  right. 
The  line  drawn  parallel  to  the  latter  furnishes  an  idea 
of  the  extent  of  the  illusion.  This  is  the  well-known 
Poggendorff  illusion.  The  upper  oblique  line  on  the 


\ 


\ 


Fig.  45.  —  The  two  diagonals 
would  meet  on  the  left  ver- 
tical line. 


Fig.  46.  —  Poggendorff's  illusion.  Which 
oblique  line  on  the  right  is  the  prolong- 
ation of  the  oblique  line  on  the  left? 


right  actually  appears  to  be  approximately  the  con- 
tinuation of  the  upper  oblique  line  on  the  right.  The 
explanation  of  this  illusion  on  the  simple  basis  of 
underestimation  or  overestimation  of  angles  is  open 
to  criticism.  If  Fig.  46  is  held  so  that  the  intercepted 
line  is  horizontal  or  vertical,  the  illusion  disappears 
or  at  least  is  greatly  reduced.  It  is  difficult  to  recon- 
cile this  disappearance  of  the  illusion  for  certain 
positions  of  the  figure  with  the  theory  that  the  illusion 
is  due  to  an  incorrect  appraisal  of  the  angles. 


86 


VISUAL  ILLUSIONS 


According  to  Judd,2  those  portions  of  the  parallels 
lying  on  the  obtuse-angle  side  of  the  intercepted  line 
will  be  overestimated  when  horizontal  or  vertical 
distances  along  the  parallel  lines  are  the  subjects  of 
attention,  as  they  are  in  the  usual  positions  of  the 
Poggendorff  figure.  He  holds  further  that  the  over- 
estimation  of  this  distance  along  the  parallels  (the 
two  vertical  lines)  and  the  underestimation  of  the 
oblique  distance  across  the  interval  are  sufficient  to 
provide  a  full  explanation  of  the  illusion.  The  dis- 
appearance and  appearance  of  the  illusion,  as  the 
position  of  the  figure  is  varied  appears  to  demonstrate 
the  fact  that  lines  produce  illusions  only  when  they 
have  a  direct  influence  on  the  direction  in  which  the 
attention  is  turned.  That  is,  when  this  Poggendorff 
figure  is  in  such  a  position  that  the  intercepted  line 
is  horizontal,  the  incorrect  estimation  of  distance  along 
the  parallels  has  no  direct  bearing  on  the  distance  to 
which  the  attention  is  directed.  In  this  case  Judd 
holds  that  the  entire  influence  of  the  parallels  is  ab- 
sorbed in  aiding  the  intercepted  line  in  carrying  the 


Fig.  47.  —  A  straight  line  appears  to  sag. 

eye  across  the  interval.    For  a  detailed  account  the 
reader  is  referred  to  the  original  paper.  ' 

Some  other  illusions  are  now  presented  to  demon- 
strate further  the  effect  of  the  presence  of  angles. 
Doubtless,  in  some  of  these,  other  causes  contribute 


THE  INFLUENCE  OF  ANGLES  87 

more  or  less  to  the  total  result.  In  Fig.  47  a  series  of 
concentric  arcs  of  circles  end  in  a  straight  line.  The 
result  is  that  the  straight  line  appears  to  sag  per- 
ceptibly. Incidentally,  it  may  be  interesting  for  the 
reader  to  ascertain  whether  or  not  there  is  any  doubt 
in  his  mind  as  to  the  arcs  appearing  to  belong  to 


Fig.  48.  —  Distortions  of  contour  due  to  contact  with  other  contours. 

circles.  To  the  author  the  arcs  appear  distorted  from 
those  of  true  circles. 

In  Fig.  48  the  bounding  figure  is  a  true  circle  but 
it  appears  to  be  distorted  or  dented  inward  where  the 
angles  of  the  hexagon  meet  it.  Similarly,  the  sides 
of  the  hexagon  appear  to  sag  inward  where  the  corners 
of  the  rectangle  meet  them. 

The  influences  which  have  been  emphasized  ap- 
parently are  responsible  for  the  illusions  in  Figs.  49, 
50  and  51.  It  is  interesting  to  note  the  disappearance 
of  the  illusion,  as  the  plane  of  Fig.  49  is  varied  from 


88 


VISUAL  ILLUSIONS 


vertical  toward  the  horizontal.  That  is,  it  is  very 
apparent  when  viewed  perpendicularly  to  the  plane  of 
the  page,  the  latter  being  held  vertically,  but  as  the 
page  is  tilted  backward  the  illusion  decreases  and 
finally  disappears. 

The  illusions  in  Figs.  50  and  51  are  commonly 


Fig.  49.  —  An  illusion  of  direction. 

termed  "  twisted  cord  "  effects.  A  cord  may  be  made 
by  twisting  two  strands  which  are  white  and  black 
(or  any  dark  color)  respectively.  This  may  be  super- 
posed upon  various  backgrounds  with  striking  results. 
In  Fig.  50  the  straight  "  cords  "  appear  bent  in  the 
middle,  owing  to  a  reversal  of  the  "  twist."  Such  a 


THE  INFLUENCE  OF  ANGLES 


89 


figure  may  be   easily  made   by  using  cord  and  a 
checkered  cloth.    In  Fig.  51  it  is  difficult  to  convince 


Fig.  50.  —  "  Twisted-cord  "  illusion.    These  are  straight  cords. 

the  intellect  that  the  "  cords  "  are  ftet£  arranged  in 
the  form  of  concentric  circles,  but  this  becomes  evi- 
dent when  one  of  them  is  traced  out.  The  influence 


Fig.  51.  —  "  Twisted-cord  "  illusion.    These  are  concentric  circles. 


90  VISUAL  ILLUSIONS 

of  the  illusion  is  so  powerful  that  it  is  even  difficult 
to  follow  one  of  the  circles  with  the  point  of  a  pencil 
around  its  entire  circumference.  The  cord  appears 
to  form  a  spiral  or  a  helix  seen  in  perspective. 

A  striking  illusion  is  obtained  by  revolving  the 
spiral  shown  in  Fig.  52  about  its  center.  This  may  be 
considered  as  an  effect  of  angles  because  the  curva- 


Fig.  52.  —  A  spiral  when  rotated  appears  to  expand  or  contract,  depending 
upon  direction  of  rotation. 

ture  and  consequently  the  angle  of  the  spiral  is  con- 
tinually changing.  There  is  a  peculiar  movement  or 
progression  toward  the  center  when  revolved  in  one 
direction.  When  the  direction  of  rotation  is  reversed 
the  movement  is  toward  the  exterior  of  the  figure; 
that  is,  there  is  a  seeming  expansion. 

Angles  appear  to  modify  our  judgments  of  the 
length  of  lines  as  well  as  of  their  direction.  Of  course, 
it  must  be  admitted  that  some  of  these  illusions  might 
be  classified  under  those  of  "  contrast "  and  others. 
In  fact,  it  has  been  stated  that  classification  is  difficult 
but  it  appears  logical  to  discuss  the  effect  of  angles 


THE  INFLUENCE  OF  ANGLES  91 

in  this  chapter  apart  from  the  divisions  presented  in 
the  preceding  chapters.  This  decision  was  reached 
because  the  effect  of  angles  could  be  seen  in  many 
of  the  illusions  which  would  more  logically  be  grouped 
under  the  classification  presented  in  the  preceding 
chapters. 

In  Fig.  53  the  three  horizontal  lines  are  of  equal 
length  but  they  appear  unequal.  This  must  be  due 
primarily  to  the  size  of  the  angles  made  by  the  lines 


Fig.53.  —  Angles  affect  the  apparent  length  of  lines. 

at  the  ends.  Within  certain  limits,  the  greater  the 
angle  the  greater  is  the  apparent  elongation  of  the 
central  horizontal  portion.  This  generalization  ap- 
pears to  apply  even  when  the  angle  is  less  than  a  right 
angle,  although  there  appears  to  be  less  strength  to 
the  illusions  with  these  smaller  angles  than  with 
the  larger  angles.  Other  factors  which  contribute  to 
the  extent  of  the  illusion  are  the  positions  of  the 
figures,  the  distance  between  them,  and  the  juxta- 
position of  certain  lines.  The  illusion  still  exists  if 
the  horizontal  lines  are  removed  and  also  if  the  figures 


92 


VISUAL  ILLUSIONS 


are  cut  out  of  paper  after  joining  the  lower  ends  of 
the  short  lines  in  each  case. 

In  Fig.  54  the  horizontal  straight  line  appears  to 
consist  of  two  lines  tilting  slightly  upward  toward 
the  center.  This  will  be  seen  to  be  in  agreement  with 
the  general  proposition  that  the  sides  of  an  angle  are 
deviated  in  the  direction  of  the  angle.  In  this  case 


A 

D 


B 


Fig.  64.  —  The  horizontal  line  appears  to  tilt  downward  toward  the  ends. 

it  should  be  noted  that  one  of  the  obtuse  angles  to 
be  considered  is  ABC  and  that  the  effect  of  this  is 
to  tilt  the  line  BD  downward  from  the  center.  In 
Fig.  55  the  horizontal  line  appears  to  tilt  upward 
toward  its  extremities  or  to  sag  in  the  middle.  The 
explanation  in  order  to  harmonize  with  the  foregoing 
must  be  based  upon  the  assumption  that  our  judg- 
ments may  be  influenced  by  things  not  present  but 


Fig.  65.  —  The  horizontal  line  appears  to  sag  in  the  middle. 

imagined.  In  this  case  only  one  side  of  each  obtuse 
angle  is  present,  the  other  side  being  formed  by  con- 
tinuing the  horizontal  line  both  ways  by  means  of 
the  imagination.  That  we  do  this  unconsciously  is 
attested  to  by  many  experiences.  For  example,  we 
often  find  ourselves  imagining  a  horizontal,  a  vertical, 
or  a  center  upon  which  to  base  a  pending  judgment. 


THE  INFLUENCE  OF  ANGLES  93 

A  discussion  of  the  influence  of  angles  must  in- 
clude a  reference  to  the  well-known  Miiller-Lyer 
illusion  presented  in  Fig.  56.  It  is  obvious  in  a  that 
the  horizontal  part  on  the  left  appears  considerably 
longer  than  that  part  in  the  right  half  of  the  diagram. 
The  influence  of  angles  in  this  illusion  can  be  easily 
tested  by  varying  the  direction  of  the  lines  at  the 
ends  of  the  two  portions. 


b 

Fig.  56.  —  The  MiiUer-Lyer  illusion. 

In  all  these  figures  the  influence  of  angles  is 
obvious.  This  does  not  mean  that  they  are  always 
solely  or  even  primarily  responsible  for  the  illusion. 
In  fact,  the  illusion  of  Poggendorff  (Fig.  46)  may  be 
due  to  the  incorrect  estimation  of  certain  linear 
distances,  but  the  angles  make  this  erroneous  judg- 
ment possible,  or  at  least  contribute  toward  it.  Many 
discussions  of  the  theories  or  explanations  of  these 
figures  are  available  in  scientific  literature  of  which 
one  by  Judd  2  may  be  taken  as  representative.  He 
holds  that  the  false  estimation  of  angles  in  the  Poggen- 
dorff figure  is  merely  a  secondary  effect,  not  always 


94  VISUAL  ILLUSIONS 

present,  and  in  no  case  the  source  of  the  illusion; 
furthermore,  that  the  illusion  may  be  explained  as 
due  to  the  incorrect  linear  distances,  and  may  be 
reduced  to  the  type  of  illusion  found  in  the  Miiller- 
Lyer  figure.  Certainly  there  are  grave  dangers  in 
explaining  an  illusion  on  the  basis  of  an  apparently 
simple  operation. 

In  Fig.  56,  b  is  made  up  of  the  two  parts  of  the 
Miiller-Lyer  illusion.  A  small  dot  may  be  placed 
equally  distant  from  the  inside  extremities  of  the  hori- 
zontal lines.  It  is  interesting  to  note  that  overesti- 
mation  of  distance  within  the  figure  is  accompanied 
with  underestimation  outside  the  figure  and,  con- 
versely, overestimation  within  the  figure  is  accom- 
panied by  underestimation  in  the  neighboring  space. 
If  the  small  dot  is  objected  to  as  providing  an  ad- 
ditional Miiller-Lyer  figure  of  the  empty  space,  this 
dot  may  be  omitted.  As  a  substitute  an  observer 
may  try  to  locate  a  point  midway  between  the  inside 
extremities  of  the  horizontal  lines.  The  error  in  locat- 
ing this  point  will  show  that  the  illusion  is  present 
in  this  empty  space. 

In  this  connection  it  is  interesting  to  note  some 
other  illusions.  In  Fig.  57  the  influence  of  several 
factors  are  evident.  Two  obviously  important  ones 
are  (1)  the  angles  made  by  the  short  lines  at  the 
extremities  of  the  exterior  lines  parallel  to  the  sides 
of  the  large  triangle,  and  (2)  the  influence  of  contrast 
of  the  pairs  of  adjacent  parallel  lines.  The  effect 
shown  in  Fig.  53  is  seen  to  be  augmented  by  the  ad- 
dition of  contrast  of  adjacent  lines  of  unequal  length. 

An  interesting  variation  of  the  effect  of  the  presence 


THE  INFLUENCE  OF  ANGLES 


95 


of  angles  is  seen  in  Fig.  58.  The  two  lines  forming 
angles  with  the  horizontal  are  of  equal  length  but  due 
to  their  relative  positions,  they  do  not  appear  so.  It 
would  be  quite  misleading  to  say  that  this  illusion  is 


\ 


Fig.  67.  —  Combined  influence  of  angles  and  contrasting  lengths. 

merely  due  to  angles.  Obviously,  it  is  due  to  the 
presence  of  the  two  oblique  lines.  It  is  of  interest 
to  turn  to  Figs.  25,  26  and  various  illusions  of  per- 
spective. 


Fig.  58.  —  Two  equal  oblique  lines  appear  unequal 
because  of  their  different  positions. 

At  this  point  a  digression  appears  to  be  necessary 
and,  therefore,  Fig.  59  is  introduced.  Here  the  areas 
of  the  two  figures  are  equal.  The  judgment  of  area  is 
likely  to  be  influenced  by  juxtaposed  lines  and  there- 
fore, as  in  this  case,  the  lower  appears  larger  than  the 


96  VISUAL  ILLUSIONS 

upper  one.  Similarly  two  trapezoids  of  equal  di- 
mensions and  areas  may  be  constructed.  If  each  is 
constructed  so  that  it  rests  upon  its  longer  parallel 
and  one  figure  is  above  the  other  and  only  slightly 
separated,  the  mind  is  tempted  to  be  influenced  by 


Fig.  69.  —  An  illusion  of  area. 

comparing  the  juxtaposed  base  of  the  upper  with 
the  top  of  the  lower  trapezoid.  The  former  dimension, 
being  greater  than  the  latterr  the  lower  figure  appears 
smaller  than  the  upper  one.  Angles  must  necessarily 
play  a  part  in  these  illusions,  although  it  is  admitted 
that  other  factors  may  be  prominent  or  even  dominant. 
This  appears  to  be  a  convenient  place  to  insert 
an  illusion  of  area  based,  doubtless,  upon  form,  but 
angles  must  play  a  part  in  the  illusions;  at  least  they 


THE  INFLUENCE  OF  ANGLES  97 

are  responsible  for  the  form.  In  Fig.  60  the  five 
figures  are  constructed  so  as  to  be  approximately 
equal  in  area.  However,  they  appear  unequal  in  this 
respect.  In  comparing  areas,  we  cannot  escape  the 
influence  of  the  length  and  directions  of  lines  which 
bound  these  areas,  and  also,  the  effect  of  contrasts 
in  lengths  and  directions.  Angles  play  a  part  in  all 
these,  although  very  indirectly  in  some  cases. 


Fig.  60.  —  Five  equal  areas  showing  the  influence  of  angles  and  contrasting 

lengths. 


To  some  extent  the  foregoing  is  a  digression  from 
the  main  intent  of  this  chapter,  but  it  appears  worth 
while  to  introduce  these  indirect  effects  of  the  presence 
of  angles  (real  or  imaginary)  in  order  to  emphasize 
the  complexity  of  influences  and  their  subtleness. 
Direction  is  in  the  last  analysis  an  effect  of  angle; 
that  is,  the  direction  of  a  line  is  measured  by  the 
angle  it  makes  with  some  reference  line,  the  latter 
being  real  or  imaginary.  In  Fig.  61,  the  effect  of 
diverting  or  directing  attention  by  some  subtle  force, 
such  as  suggestion,  is  demonstrated.  This  "  force  " 
appears  to  contract  or  expand  an  area.  The  circle 
on  the  left  appears  smaller  than  the  other.  Of  course 
there  is  the  effect  of  empty  space  compared  with 
partially  filled  space,  but  this  cannot  be  avoided  in 


98  VISUAL  ILLUSIONS 

this  case.  However,  it  can  be  shown  that  the  sug- 
gestions produced  by  the  arrows  tend  to  produce 
apparent  reduction  or  expansion  of  areas.  Note  the 
use  of  arrows  in  advertisements. 

Although  theory  is  subordinated  to  facts  in  this 
book,  a  glimpse  here  and  there  should  be  interesting 
and  helpful.  After  having  been  introduced  to  various 
types  and  influences,  perhaps  the  reader  may  better 


Fig.  61.  —  Showing  the  effect  of  directing  the  attention. 

grasp  the  trend  of  theories.  The  perspective  theory 
assumes,  and  correctly  so,  that  simple  diagrams  often 
suggest  objects  in  three  dimensions,  and  that  the 
introduction  of  an  imaginary  third  dimension  effects 
changes  in  the  appearance  of  lines  and  angles.  That 
is,  lengths  and  directions  of  lines  are  apparently 
altered  by  the  influence  of  lines  and  angles,  which 
do  not  actually  exist.  That  this  is  true  may  be  proved 
in  various  cases.  In  fact  the  reader  has  doubtless 


THE  INFLUENCE  OF  ANGLES  99 

been  convinced  of  this  in  connection  with  some  of 
the  illusions  already  discussed.  Vertical  lines  often 
represent  lines  extending  away  from  the  observer, 
who  sees  them  foreshortened  and  therefore  they 
may  seem  longer  than  horizontal  lines  of  equal  length, 
which  are  not  subject  to  foreshortening.  This  could 
explain  such  illusions  as  seen  in  Figs.  4  and  5.  How- 
ever this  theory  is  not  as  easily  applied  to  many  il- 
lusions. 

According  to  Thiery's  perspective  theory  a  line 
that  appears  nearer  is  seen  as  smaller  and  a  line 
that  seems  to  be  further  away  is  perceived  as  longer. 
If  the  left  portion  of  &,  Fig.  56,  be  reproduced  with 
longer  oblique  lines  at  the  ends  but  with  the  same 
length  of  horizontal  lines,  it  will  appear  closer  and 
the  horizontal  lines  will  be  judged  as  shorter.  The 
reader  will  find  it  interesting  to  draw  a  number  of 
these  portions  of  the  Miiller-Lyer  figure  with  the 
horizontal  line  in  each  case  of  the  same  length  but 
with  longer  and  longer  obliques  at  the  ends. 

The  dynamic  theory  of  Lipps  gives  an  important 
role  to  the  inner  activity  of  the  observer,  which  is  not 
necessarily  separated  from  the  objects  viewed,  but 
may  be  felt  as  being  in  the  objects.  That  is,  in  view- 
ing a  figure  the  observer  unconsciously  separates  it 
from  surrounding  space  and  therefore  creates  some- 
thing definite  in  the  latter,  as  a  limiting  activity. 
These  two  things,  one  real  (the  object)  and  one  im- 
aginary, are  balanced  against  each  other.  A  vertical 
line  may  suggest  a  necessary  resistance  against 
gravitational  force,  with  the  result  that  the  line  ap- 
pears longer  than  a  horizontal  one  resting  in  peace. 


100  VISUAL  ILLUSIONS 

The  difficulty  with  this  theory  is  that  it  allows  too 
much  opportunity  for  purely  philosophical  explanations, 
which  are  likely  to  run  to  the  fanciful.  It  has  the 
doubtful  advantage  of  being  able  to  explain  illusions 
equally  well  if  they  are  actually  reversed  from  what 
they  are.  For  example,  gravity  could  either  contract 
or  elongate  the  vertical  line,  depending  upon  the 
choice  of  viewpoint. 

The  confusion  theory  depends  upon  attention  and 
begins  with  the  difficulty  of  isolating  from  illusory 
figures  the  portions  to~4>e  judged.  Amid  the  com- 
plexity of  the  figure  the  attention  cannot  easily  be 
fixed  on  the  portions  to  be  judged.  This  results  in 
confusion.  For  example,  if  areas  of  different  shapes 
such  as  those  in  Fig.  60  are  to  be  compared,  it  is 
difficult  to  become  oblivious  of  form  or  of  compact- 
ness. In  trying  to  see  the  two  chief  parallel  lines  in 
Fig.  38,  in  their  true  parallelism  the  attention  is  being 
subjected  to  diversion,  by  the  short  oblique  parallels 
with  a  compromising  result.  Surely  this  theory 
explains  some  illusions  successfully,  but  it  is  not  so 
successful  with  some  of  the  illusions  of  contrast. 
The  fact  that  practice  in  making  judgments  in  such 
cases  as  Figs.  45  and  56  reduces  the  illusion  even  to 
ultimate  disappearance,  argues  in  favor  of  the  con- 
fusion theory.  Perhaps  the  observer  devotes  himself 
more  or  less  consciously  to  isolating  the  particular 
feature  to  be  judged  and  finally  attains  the  ability  to 
do  so.  According  to  Auerbach's  indirect-vision  theory 
the  eyes  in  judging  the  two  halves  of  the  horizontal 
line  in  a,  Fig.  56,  involuntarily  draw  imaginary  lines 
parallel  to  this  line  but  above  or  below  it.  Obviously 


THE  INFLUENCE  OF  ANGtS  101 

the  two  parts  of  such  lines  are  unequal  in  the  same 
manner  as  the  horizontal  line  in  the  Miiller-Lyer 
figure  appears  divided  into  two  unequal  parts. 

Somewhat  analogous  to  this  in  some  cases  is 
Brunot's  mean-distance  theory.  According  to  this  we 
establish  "  centers  of  gravity  "  in  figures  and  these 
influence  our  judgments. 

These  are  glimpses  of  certain  trends  of  theories. 
None  is  a  complete  success  or  failure.  Each  explains 
some  illusions  satisfactorily,  but  not  necessarily  ex- 
clusively. For  the  present,  we  will  be  content  with 
these  glimpses  of  the  purely  theoretical  aspects  of 
visual  illusions. 


VII 
ILLUSIONS   OF  DEPTH  AND   OF  DISTANCE 

BESIDES  the  so-called  geometrical  illusions  dis- 
cussed in  the  preceding  chapters,  there  is  an 
interesting  group  in  which  the  perception  of 
the  third  dimension  is  in  error.  When  any  of  the 
ordinary  criteria  of  relief  or  of  distance  are  apparently 
modified,  illusions  of  this  kind  are  possible.  There 
are  many  illusions  of  this  sort,  such  as  the  looming  of 
objects  in  a  fog;  the  apparent  enlargement  of  the 
sun  and  moon  near  the  horizon;  the  flattening  of 
the  "vault"  of  the  sky;  the  intaglio  seen  as  relief; 
the  alteration  of  relief  with  lighting ;  and  various 
changes  in  the  landscape  when  regarded  with  the 
head  inverted. 

Although  some  of  the  criteria  for  the  perception 
of  depth  or  of  distance  have  already  been  pointed 
out,  especially  in  Chapter  III,  these  will  be  mentioned 
again.  Distance  or  depth  is  indicated  by  the  dis- 
tribution of  light  and  shade,  and  an  unusual  object 
like  an  intaglio  is  likely  to  be  mistaken  for  relief 
which  is  more  common.  An  analysis  of  the  lighting 
will  usually  reveal  the  real  form  of  the  object.  (See 
Figs.  70,  71,  72,  73,  76  and  77.)  In  this  connection 
it  is  interesting  to  compare  photographic  negatives 
with  their  corresponding  positive  prints. 

Distance    is    often    estimated    by    the    definition 

and  color  of  objects  seen  through  great  depths  of 

102 


ILLUSIONS  OF  DEPTH  AND  OF  DISTANCE      103 

air  (aerial  perspective).  These  distant  objects  are 
"  blurred  "  by  the  irregular  refraction  of  the  light- 
rays  through  non-homogeneous  atmosphere.  They  are 
obscured  to  some  degree  by  the  veil  of  brightness  due 
to  the  illuminated  dust,  smoke,  etc.,  in  the  atmosphere. 
They  are  also  tinted  (apparently)  by  the  superposition 
of  a  tinted  atmosphere.  Thus  we  have  "  dim 
distance,"  "  blue  peaks,"  "  azure  depths  of  sky," 
etc.,  represented  in  photographs,  paintings,  and  writ- 
ings. Incidentally,  the  sky  above  is  blue  for  the 
same  general  reasons  that  the  atmosphere,  interven- 
ing between  the  observer  and  a  distant  horizon,  is 
bluish.  The  ludicrous  errors  made  in  estimating 
distances  in  such  regions  as  the  Rockies  is  usually 
accounted  for  by  the  rare  clearness  and  homogeneity 
of  the  atmosphere.  However,  is  the  latter  a  full 
explanation?  To  some  extent  we  judge  unknown  size 
by  estimated  distance,  and  unknown  distance  by 
estimated  size.  When  a  person  is  viewing  a  great 
mountain  peak  for  the  first  time,  is  he  not  likely  to 
assume  it  to  be  comparable  in  size  to  the  hills  with 
which  he  has  been  familiar?  Even  by  allowing  con- 
siderable, is  he  not  likely  to  greatly  underestimate 
the  size  of  the  mountain  and,  as  a  direct  consequence, 
to  underestimate  the  distance  proportionately?  This 
incorrect  judgment  would  naturally  be  facilitated  by 
the  absence  of  "  dimness  "  and  "  blueness  "  due  to 
the  atmospheric  haze. 

Angular  perspective,  which  apparently  varies  the 
forms  of  angles  and  produces  the  divergence  of  lines, 
contributes  much  information  in  regard  to  relative 
and  absolute  distances  from  the  eye  of  the  various 


104  VISUAL  ILLUSIONS 

objects  or  the  parts  of  an  object.  For  example,  a 
rectangle  may  appear  as  a  rhomboid.  It  is  obvious 
that  certain  data  pertaining  to  the  objects  viewed 
must  be  assumed,  and  if  the  assumptions  are  incorrect, 
illusions  will  result.  These  judgments  also  involve, 
as  most  judgments  do,  other  data  external  to  the 
objects  viewed.  Perhaps  these  incorrect  judgments 
are  delusions  rather  than  illusions,  because  visual 
perception  has  been  deluded  by  misinformation  sup- 
plied by  the  intellect. 

Size  or  linear  perspective  is  a  factor  in  the  per- 
ception of  depth  or  of  distance.  As  has  been  stated, 
if  we  know  the  size  experience  determines  the  distance; 
and  conversely,  if  we  know  the  distance  we  may 
estimate  the  size.  Obviously  estimates  are  involved 
and  these  when  incorrect  lead  to  false  perception  or 
interpretation. 

As  an  object  approaches,  the  axes  of  the  eyes 
converge  more  and  more  and  the  eye-lens  must  be 
thickened  more  and  more  to  keep  the  object  in  focus. 
As  stated  in  Chapter  III,  we  have  learned  to  interpret 
these  accompanying  sensations  of  muscular  adjust- 
ment. This  may  be  demonstrated  by  holding  an  ob- 
ject at  an  arm's  length  and  then  bringing  it  rapidly 
toward  the  eyes,  keeping  it  in  focus  all  the  time.  The 
sensations  of  convergence  and  accommodation  are 
quite  intense. 

The  two  eyes  look  at  a  scene  from  two  different 
points  of  view  respectively  and  then:  images  do  not 
perfectly  agree,  as  has  been  shown  hi  Figs.  2  and  3. 
This  binocular  disparity  is  responsible  to  some  degree 
for  the  perception  of  depth,  as  the  stereoscope  has 


ILLUSIONS  OF  DEPTH  AND  OF  DISTANCE      105 

demonstrated.  If  two  spheres  of  the  same  size  are 
suspended  on  invisible  strings,  one  at  six  feet,  the 
other  at  seven  feet  away,  one  eye  sees  the  two  balls 
in  the  same  plane,  but  one  appears  larger  than  the 
other.  With  binocular  vision  the  balls  appear  at 
different  distances,  but  judgment  appraises  them  as 
of  approximately  equal  size.  At  that  distance  the 
focal  adjustment  is  not  much  different  for  both  balls, 
so  that  the  muscular  movement,  due  to  focusing  the 
eye,  plays  a  small  part  in  the  estimation  of  the  rela- 
tive distance.  Binocular  disparity  and  convergence 
are  the  primary  factors. 

Some  have  held  that  the  perception  of  depth, 
that  is,  of  a  relative  distance,  arises  from  the  process 
of  unconsciously  running  the  point  of  sight  back  and 
forth.  However,  this  view,  unmodified,  appears  un- 
tenable when  it  is  considered  that  a  scene  illuminated 
by  a  lightning  flash  (of  the  order  of  magnitude  of  a 
thousandth  of  a  second)  is  seen  even  in  this  brief 
moment  to  have  depth.  Objects  are  seen  in  relief, 
in  actual  relation  as  to  distance  and  in  normal  per- 
spective, even  under  the  extremely  brief  illumination 
of  an  electric  spark  (of  the  order  of  magnitude  of  one 
twenty-thousandth  of  a  second).  This  can  also  be 
demonstrated  by  viewing  stereoscopic  pictures  with  a 
stereoscope,  the  illumination  being  furnished  by  an 
electric  spark.  Under  these  circumstances  relief  and 
perspective  are  quite  satisfactory.  Surely  in  these 
brief  intervals  the  point  of  sight  cannot  do  much 
surveying  of  a  scene. 

Parallax  aids  in  the  perception  of  depth  or 
distance.  If  the  head  be  moved  laterally  the  view  or 


106  VISUAL  ILLUSIONS 

scene  changes  slightly.  Objects  or  portions  of  ob- 
jects previously  hidden  by  others  may  now  become 
visible.  Objects  at  various  distances  appear  to  move 
nearer  or  further  apart.  We  have  come  to  interpret 
these  apparent  movements  of  objects  in  a  scene  in 
terms  of  relative  distances;  that  is,  the  relative 
amount  of  parallactic  displacement  is  a  measure  of 
the  relative  distances  of  the  objects. 

The  relative  distances  or  depth  locations  of  differ- 
ent parts  of  an  object  can  be  perceived  as  fluctuating 
or  even  reversing.  This  is  due  to  fluctuations  in 
attention,  and  illusions  of  reversible  perspective  are  of 
this  class.  It  is  quite  impossible  for  one  to  fix  his 
attention  in  perfect  continuity  upon  any  object.  There 
are  many  involuntary  eye-movements  which  cannot 
be  overcome  and  under  normal  conditions  certain 
details  are  likely  to  occupy  the  focus  of  attention 
alternately  or  successively.  fcThis  applies  equally  well 
to  the  auditory  sense  and  perhaps  to  the  other  senses. 
Emotional  coloring  has  much  to  do  with  the  fixation 
of  attention;  that  which  we  admire,  desire,  love, 
hate,  etc.,  is  likely  to  dwell  more  in  the  focus  of  at- 
tention than  that  which  stirs  our  emotions  less. 

A  slight  suggestion  of  forward  and  backward 
movements  can  be  produced  by  successively  inter- 
cepting the  vision  of  one  eye  by  an  opaque  card  or 
other  convenient  object.  It  has  been  suggested  that 
the  illusion  is  due  to  the  consequent  variations  in  the 
tension  of  convergence.  Third  dimensional  move- 
ments may  be  produced  for  binocular  or  monocular 
vision  during  eye-closure.  They  are  also  produced  by 
opening  the  eyes  as  widely  as  possible,  by  pressure  on 


ILLUSIONS  OF  DEPTH  AND  OF  DISTANCE      107 

the  eye-balls,  and  by  stressing  the  eyelids.  However, 
these  are  not  important  and  are  merely  mentioned  in 
passing. 

An  increase  in  the  brightness  of  an  object  is  ac- 
companied by  an  apparent  movement  toward  the  ob- 
server, and  conversely  a  decrease  in  brightness 
produces  an  apparent  movement  in  the  opposite  di- 
rection. These  effects  may  be  witnessed  upon  view- 
ing the  glowing  end  of  a  cigar  which  is  being  smoked 
by  some  one  a  few  yards  away  in  the  darkness. 
Rapidly  moving  thin  clouds  may  produce  such  an 
effect  by  varying  the  brightness  of  the  moon.  Some 
peculiar  impressions  of  this  nature  may  be  felt  while 
watching  the  flashing  light  of  some  light-houses  or  of 
other  signaling  stations.  It  has  been  suggested  that 
we  naturally  appraise  brighter  objects  as  nearer  than 
objects  less  bright.  However,  is  it  not  interesting  to 
attribute  the  apparent  movement  to  irradiation?  (See 
Chapter  VIII.)  A  bright  object  appears  larger  than  a 
dark  object  of  the  same  size  and  at  the  same  distance. 
When  the  same  object  varies  in  brightness  it  remains 
in  consciousness  the  same  object  and  therefore  of 
constant  size;  however,  the  apparent  increase  in  size 
as  it  becomes  brighter  must  be  accounted  for  in  some 
manner  and  there  is  only  one  way  open.  It  must  be 
attributed  a  lesser  distance  than  formerly  and  there- 
fore the  sudden  increase  in  brightness  mediates  a 
consciousness  of  a  movement  forward,  that  is,  toward 
the  observer. 

If  two  similay  objects,  such  as  the  points  of  a 
compass,  are  viewed  binocularly  and  their  lateral 
distance  apart  is  altered,  the  observer  is  conscious  of 


108  VISUAL  ILLUSIONS 

a  third  dimensional  movement.  Inasmuch  as  the 
accommodation  is  unaltered  but  convergence  must 
be  varied  as  the  lateral  distance  between  the  two, 
the  explanation  of  the  illusion  must  consider  the 
latter.  The  pair  of  compass-points  are  very  con- 
venient for  making  a  demonstration  of  this  pronounced 
illusion.  The  relation  of  size  and  distance  easily 
accounts  for  the  illusion. 

Obviously  this  type  of  illusion  cannot  be  illustrated 
effectively  by  means  of  diagrams,  so  the  reader  must 
be  content  to  watch  for  them  himself.  Some  persons 
are  able  voluntarily  to  produce  illusory  movements  in 
the  third  dimension,  but  such  persons  are  rare.  Many 
persons  have  experienced  involuntary  illusions  of 
depth.  Carr  found,  in  a  series  of  classes  comprising 
350  students,  58  persons  who  had  experienced  in- 
voluntary depth  illusions  at  some  time  in  their  lives. 
Five  of  these  also  possessed  complete  voluntary 
control  over  the  phenomenon.  The  circumstances 
attending  visual  illusions  of  depth  are  not  the  same 
for  various  cases,  and  the  illusions  vary  widely  in 
their  features. 

Like  other  phases  of  the  subject,  this  has  been 
treated  in  many  papers,  but  of  these  only  one  will  be 
specifically  mentioned,  for  it  will  suffice.  Carr  3  has 
studied  this  type  of  illusion  comparatively  recently 
and  apparently  quite  generally,  and  his  work  will  be 
drawn  upon  for  examples  of  this  type.  Apparently 
they  may  be  divided  into  four  classes:  (1)  Those  of 
pure  distance;  that  is,  an  object  may  appear  to  be 
located  at  varying  distances  from  the  observer,  but  no 
movement  is  perceived.  For  example,  a  person 


ILLUSIONS   OF  DEPTH  AND   OF  DISTANCE       109 

might  be  seen  first  at  the  true  distance;  he  might 
be  seen  next  very  close  in  front  of  the  eyes;  then 
he  might  suddenly  appear  to  be  quite  remote;  (2)  il- 
lusions of  pure  motion;  that  is,  objects  are  perceived 
as  moving  in  a  certain  direction  without  any  apparent 
change  in  location.  In  other  words,  they  appear  to 
move,  but  they  do  not  appear  to  traverse  space;  (3)  il- 
lusions of  movement  which  include  a  change  in  lo- 
cation. This  appears  to  be  the  most  common  illusion 
of  depth;  (4)  those  including  a  combination  of  the 
first  and  third  classes.  For  example,  the  object 
might  first  appear  to  move  away  from  its  true  location 
and  is  perceived  at  some  remote  place.  Shortly  it  may 
appear  in  its  true  original  position,  but  this  change 
in  location  does  not  involve  any  sense  of  motion. 

These  peculiar  illusions  of  depth  are  not  as  gener- 
ally experienced  as  those  described  in  preceding 
chapters.  A  geometrical  illusion,  especially  if  it  is 
pronounced,  is  likely  to  be  perceived  quite  univer- 
sally, but  these  illusions  of  depth  are  either  more  diffi- 
cult to  notice  or  more  dependent  upon  psychological 
peculiarities  far  from  universal  among  people.  It  is 
interesting  to  note  the  percentages  computed  from 
Carr's  statistics  obtained  upon  interrogating  350  stu- 
dents. Of  these,  17  per  cent  had  experienced  depth- 
illusions  and  between  one  and  two  per  cent  had  volun- 
tary control  of  the  phenomenon.  Of  the  48  who  had 
experienced  illusions  of  this  type  and  were  able  to 
submit  detailed  descriptions,  25  per  cent  belonged  to 
class  (1)  of  those  described  in  the  preceding  para- 
graph; 4  per  cent  to  class  (2);  52  per  cent  to  class 
(3);  and  17  per  cent  to  class  (4). 


110  VISUAL  ILLUSIONS 

Usually  the  illusion  involves  all  objects  in  the 
visual  field  but  with  some  subjects  the  field  is  con- 
tracted or  the  objects  in  the  periphery  of  the  field 
are  unaffected.  For  most  persons  these  illusions  in- 
volve normal  perceptual  objects,  although  it  appears 
that  they  are  phases  of  hallucinatory  origin. 

Inasmuch  as  these  illusions  cannot  be  illustrated 
diagrammatically  we  can  do  no  better  than  to  condense 
some  of  the  descriptions  obtained  and  reported  by 
Carr.3 

A  case  in  which  the  peripheral  objects  remain 
visible  and  stationary  at  their  true  positions  while  the 
central  portion  of  the  field  participates  in  the  illusion 
is  as  follows: 

The  observer  on  a  clear  day  was  gazing  down  a  street  which 
ended  a  block  away,  a  row  of  houses  forming  the  background 
at  the  end  of  the  street.  The  observer  was  talking  to  and  look- 
ing directly  at  a  companion  only  a  short  distance  away.  Soon 
this  person  (apparently)  began  to  move  down  the  street,  until 
she  reached  the  background  of  houses  at  the  end,  and  then 
slowly  came  back  to  her  original  position.  The  movement  in 
both  directions  was  distinctly  perceived.  During  the  illusory 
movement  there  was  no  vagueness  of  outline  or  contour,  no 
blurring  or  confusion  of  features;  the  person  observed,  seemed 
distinct  and  substantial  hi  character  during  the  illusion.  The 
perceived  object  moved  in  relation  to  surrounding  objects ;  there 
was  no  movement  of  the  visual  field  as  a  whole.  The  person 
decreased  in  size  during  the  backward  movement  and  increased 
in  size  during  the  forward  return  movement. 

With  many  persons  who  experience  illusions  of 
depth,  the  objects  appear  to  move  to,  or  appear  at, 
some  definite  position  and  remain  there  until  the  il- 
lusion is  voluntarily  overcome,  or  until  it  disappears 
without  voluntary  action.  A  condensation  of  a  typical 


ILLUSIONS  OF  DEPTH  AND  OF  DISTANCE       111 

description  of  this  general  type  presented  by  Carr  is 
as  follows: 

All  visual  objects  suddenly  recede  to  the  apparent  distance 
of  the  horizon  and  remain  in  that  position  several  minutes,  re- 
turning at  the  end  of  this  period  to  their  original  positions.  This 
return  movement  is  very  slow  at  the  beginning,  but  the  latter 
phase  of  the  movement  is  quite  rapid.  If  the  subject  closes 
her  eyes  while  the  objects  appear  at  their  distant  position  she 
cannot  even  imagine  those  objects  located  anywhere  except  at 
their  apparent  distant  position. 

In  all  cases  (encountered  by  Carr)  the  motion  in  both  di- 
rections is  an  actual  experience  reality  and  the  subject  was 
helpless  as  to  initiating,  stopping,  or  modifying  the  course  of  the 
illusion  in  any  way.  Objects  and  even  visual  images  (which 
are  subject  to  the  same  illusions)  decrease  in  size  in  proportion 
to  the  amount  of  backward  movement  and  grow  larger  again  on 
their  return  movement.  The  objects  are  always  clearly  defined 
as  if  in  good  focus.  In  this  particular  case  the  illusion  occurred 
about  twice  a  year,  under  a  variety  of  conditions  of  illumination, 
at  various  tunes  of  the  day,  but  apparently  under  conditions  of 
a  rather  pronounced  fatigue. 

In  regard  to  the  variation  in  the  size  of  objects, 
many  who  have  experienced  these  illusions  of  depth 
testify  that  the  size  seems  to  change  in  proportion  to 
the  apparent  distance,  according  to  the  law  of  per- 
spective. Some  persons  appear  in  doubt  as  to  this 
change  and  a  few  have  experienced  the  peculiar 
anomaly  of  decreasing  size  as  the  objects  apparently 
approached. 

Many  persons  who  have  experienced  these  pe- 
culiar illusions  report  no  change  in  the  distinctness  of 
objects;  almost  as  many  are  uncertain  regarding  this 
point;  and  as  many  report  a  change  in  distinctness. 
Apparently  there  are  phases  of  hallucinatory  origin 


112  VISUAL  ILLUSIONS 

so  that  there  is  a  wide  variety  of  experiences  among 
those  subject  to  this  type  of  illusion. 

According  to  Carr's  investigation  internal  con- 
ditions alone  are  responsible  for  the  illusion  with 
more  persons  than  those  due  to  external  conditions 
alone.  With  some  persons  a  combination  of  internal 
and  external  conditions  seem  to  be  a  necessity.  Fix- 
ation of  vision  appears  to  be  an  essential  objective 
condition  for  many  observers.  That  is,  the  illusion 
appeared  while  fixating  a  speaker  or  singer  in  a  church 
or  a  theater.  With  others  the  illusion  occurs  while 
reading.  Some  reported  that  fixation  upon  checkered 
or  other  regularly  patterned  objects  was  an  essential 
condition.  Among  the  subjective  conditions  reported 
as  essential  are  steady  fixation,  concentration  of  at- 
tention, complete  mental  absorption,  dreamy  mental 
abstraction,  and  fatigue. 

Ocular  defects  do  not  appear  to  be  essential,  for 
the  illusions  have  been  experienced  by  many  whose 
eyes  were  known  to  be  free  from  any  abnormalities. 

Period  of  life  does  not  appear  to  have  any  primary 
influence,  for  those  who  are  subject  to  these  peculiar 
illusions  often  have  experienced  them  throughout 
many  years.  In  some  cases  it  is  evident  that  the 
illusions  occur  during  a  constrained  eye  position, 
while  lying  down,  immediately  upon  arising  from 
bed  in  the  morning,  and  upon  opening  the  eyes  after 
having  had  them  closed  for  some  time.  However, 
the  necessity  for  these  conditions  are  exceptional. 

The  control  of  these  illusions  of  depth,  that  is, 
the  ability  to  create  or  to  destroy  them,  appears  to 
be  totally  lacking  for  most  of  those  who  have  ex- 


ILLUSIONS  OF  DEPTH  AND  OF  DISTANCE       113 

perienced  them.  Some  can  influence  them,  a  few 
can  destroy  them,  a  few  can  indirectly  initiate  them, 
but  those  who  can  both  create  and  destroy  them  ap- 
pear to  be  rare. 

It  may  seem  to  the  reader  that  the  latter  part  of 
this  chapter  departs  from  the  main  trend  of  this  book, 
for  most  of  these  illusions  of  depth  are  to  a  degree 
of  hallucinatory  origin.  Furthermore  it  has  been  the 
intention  to  discuss  only  those  types  of  illusions 
which  are  experienced  quite  uniformly  and  univer- 
sally. The  digression  of  this  chapter  is  excused  on 
the  basis  of  affording  a  glimpse  along  the  borderland 
of  those  groups  of  illusions  which  are  nearly  uni- 
versally experienced.  Many  other  phases  of  depth 
illusions  have  been  recorded  in  scientific  literature. 
The  excellent  records  presented  by  Carr  could  be 
drawn  upon  for  further  glimpses,  but  it  appears  that 
no  more  space  should  be  given  to  this  exceptional 
type.  The  reader  should  be  sufficiently  forewarned 
of  this  type  and  should  be  able  to  take  it  into  account 
if  peculiarities  in  other  types  appear  to  be  explainable 
in  this  manner.  However,  in  closing  it  is  well  to 
emphasize  the  fact  that  the  hallucinatory  aspect  of 
depth  illusions  is  practically  absent  in  types  of  il- 
lusions to  which  attention  is  confined  in  other  chapters. 


VIII 
IRRADIATION  AND  BRIGHTNESS-CONTRAST 

MANY  interesting  and  striking  illusions  owe 
their  existence  to  contrasts  in  brightness. 
The  visual  phenomenon  of  irradiation  does 
not  strictly  belong  to  this  group,  but  it  is  so  closely 
related  to  it  and  so  dependent  upon  brightness- 
contrast  that  it  is  included.  A  dark  line  or  spot  will 
appear  darker  in  general  as  the  brightness  of  its 
environment  is  increased;  or  conversely,  a  white  spot 
surrounded  by  a  dark  environment  will  appear  brighter 
as  the  latter  is  darkened.  In  other  words,  black  and 
white,  when  juxtaposed,  mutually  reinforce  each 
other.  Black  print  on  a  white  page  appears  much 
darker  than  it  really  is.  This  may  be  proved  by 
punching  a  hole  in  a  black  velvet  cloth  and  laying 
this  hole  over  a  "  black  "  portion  of  a  large  letter. 
The  ink  which  appeared  so  black  in  the  print,  when 
the  latter  was  surrounded  by  the  white  paper,  now 
appears  only  a  dark  gray.  Incidentally  a  hole  in  a 
box  lined  with  black  velvet  is  much  darker  than  a 
piece  of  the  black  velvet  surrounding  the  hole. 

The  effects  of  brightness-contrast  are  particularly 
striking  when  demonstrated  by  means  of  lighting,  a 
simple  apparatus  being  illustrated  diagrammatically 
in  Fig.  62.  For  example,  if  a  hole  H  is  cut  in  an  opaque 
white  blotting  paper  and  a  large  piece  of  the  white 

114 


IRRADIATION  AND  BRIGHTNESS -CONTRAST       116 


blotting  paper  is  placed  at  C,  the  eye  when  placed 
before  the  opening  at  the  right  will  see  the  opening 
at  H  filled  with  the  background  C.  The  hole  H  may 
be  cut  in  thin  metal,  painted  a  dull  white,  and  may 
be  of  the  shape  of  a  star.  This  shape  provides  an 
intimacy  between  the  hole  and  its  environment 
which  tends  to  augment  the  effects  of  contrasts.  R 
and  F  are  respectively  the  rear  and  front  lamps. 


X 


Fig.  62. —  Simple  apparatus  for  demonstrating 

the  remarkable  effects  of  contrasts 

in  brightness  and  color. 

That  is,  the  lamps  R  illuminate  C,  which  "fills  "  the 
hole  and  apparently  is  the  hole;  and  the  lamps  F 
illuminate  the  diffusing  white  environment  E.  The 
two  sets  of  lamps  may  be  controlled  by  separate 
rheostats,  but  if  the  latter  are  unavailable  the  lamps 
(several  in  each  set)  may  be  arranged  so  that  by 
turning  each  one  off  or  on,  a  range  of  contrasts  in 
brightness  between  E  and  H  (in  reality  C)  may  be 
obtained.  (By  using  colored  lamps  and  colored  papers 
as  discussed  in  Chapter  IX  the  marvelous  effects  of 
color-contrast  may  be  superposed  upon  those  of 
brightness-contrast.) 


116  VISUAL  ILLUSIONS 

If,  for  example,  C  is  very  feebly  illuminated  and 
E  is  very  bright,  C  will  be  pronounced  black;  but 
when  the  lamps  F  are  extinguished  and  no  light  is 
permitted  to  reach  E,  the  contrast  is  reversed,  and 
C  may  actually  appear  "  white."  Of  course,  it  is 
obvious  that  white  and  black  are  relative  terms  as 
encountered  in  such  a  case.  In  fact  in  brightness- 
contrasts  relative  and  not  absolute  values  of  bright- 
ness are  usually  the  more  important.  In  order  to 
minimize  the  stray  light  which  emerges  from  JfJ,  it  is 
well  to  paint  the  inside  of  both  compartments  black 
with  the  exception  of  sufficiently  large  areas  of  C  and 
E.  The  use  of  black  velvet  instead  of  black  paint  is 
sometimes  advisable.  It  is  also  well  to  screen  the 
lamps  as  suggested  in  the  diagram.  This  simple 
apparatus  will  demonstrate  some  very  striking  effects 
of  contrasts  in  brightness  and  will  serve,  also,  to 
demonstrate  even  more  interesting  effects  of  contrasts 
in  color. 

Two  opposite  contrasts  obtainable  by  means  of  a 
simple  apparatus  illustrated  in  Fig.  62  may  be  shown 
simultaneously  by  means  of  white,  black,  and  gray 
papers  arranged  as  in  Fig.  63.  In  this  figure  the  gray 
is  represented  by  the  partially  black  7s,  each  of  which 
contains  equal  amounts  of  black  and  of  white.  When 
held  at  some  distance  this  serves  as  a  gray  and  the 
same  effect  is  apparent  as  is  described  for  the  case  of 
actually  gray  7s.  An  excellent  demonstration  may 
be  made  by  the  reader  by  using  two  7s,  cut  from  the 
same  sheet  of  gray  paper,  and  pasted  respectively  upon 
white  and  black  backgrounds,  as  in  Fig.  63.  It  will 
be  apparent  that  the  one  amid  the  black  environment 


IRRADIATION  AND  BRIGHTNESS  -  CONTRAST      117 

appears  much  brighter  than  the  one  (same  gray) 
amid  the  white  environment.  This  can  be  demon- 
strated easily  to  an  audience  by  means  of  a  figure 
two  feet  long.  It  is  interesting  to  carry  the  experiment 
further  and  place  a  V  of  much  darker  gray  on  the 
black  background  than  the  V  on  the  white  back- 
ground. The  persistency  of  the  illusion  is  found  to 
be  remarkable,  for  it  will  exist  even  when  the  one  V 


Fig.  63.  —  Illustrating  brightness-contrast. 

is  actually  a  much  darker  gray  than  the  other.  To 
become  convinced  that  the  two  grays  are  of  the  same 
brightness  in  Fig.  63,  it  is  only  necessary  to  punch 
two  holes  in  a  white  or  gray  card  at  such  a  distance 
apart  that  they  will  lie  respectively  over  portions  of 
the  two  Vs  when  the  card  is  laid  upon  Fig.  63.  The 
grays  in  the  holes  should  now  appear  alike  because 
their  environments  are  similar. 

The  importance  of  contrasts  in  brightness  and  in 
color  cannot  be  overemphasized,  and  it  appears  certain 


118  VISUAL  ILLUSIONS 

that  no  one  can  fully  realize  their  effectiveness  with- 
out witnessing  it  in  a  manner  similar  to  that  sug- 
gested in  Fig.  62. 

Many  illusions  of  brightness-contrast  are  visible 
on  every  hand.    For  example,  the  point  at  which  the 


Fig.  64.  —  An  effect  of  brightness-contrast.    Note 

the  darkening  of  the  intersections 

of  the  white  strips. 

mullions  of  a  window  cross  will  be  seen  to  appear 
brighter  than  the  remaining  portions  of  them  when 
viewed  against  a  bright  sky.  Conversely,  in  Fig.  64, 
dark  spots  appear  where  the  white  bars  cross.  This 
is  purely  an  illusion  and  the  same  type  may  be  wit- 
nessed by  the  observant  many  times  a  day.  In  Fig.  64 
it  is  of  interest  to  note  that  the  illusion  is  weak  for 
the  crossing  upon  which  the  point  of  sight  rests,  but 
by  averted  vision  the  illusion  is  prominent  for  the 


IRRADIATION  AND  BRIGHTNESS -CONTRAST      119 

other  crossings.  This  is  one  of  the  effects  which 
depends  upon  the  location  in  the  visual  field. 

No  brightness-contrasts  are  seen  correctly  and 
often  the  illusions  are  very  striking.  If  a  series  of 
gray  papers  is  arranged  from  black  to  white,  with  the 
successive  pieces  overlapped  or  otherwise  juxtaposed, 
a  series  of  steps  of  uniform  brightness  is  not  seen. 
An  instrument  would  determine  the  brightness  of 
each  as  uniform,  but  to  the  eye  the  series  would  ap- 
pear somewhat  "fluted."  That  is,  where  a  light  gray 
joined  a  darker  gray  the  edge  of  the  former  would 
appear  lighter  than  its  actual  brightness,  and  the  edge 
of  the  darker  gray  would  appear  darker  than  it  should. 
This  may  also  be  demonstrated  by  laying  a  dozen 
pieces  of  white  tissue  paper  in  a  pile  in  such  a  manner 
that  a  series  of  1,  2,  3,  4,  etc.,  thickness  would  be 
produced.  On  viewing  this  by  transmitted  light  a 
series  of  grays  is  seen,  and  the  effect  of  contrast  is 
quite  apparent.  Such  a  pattern  can  be  made  photo- 
graphically by  rotating  before  a  photographic  plate  a 
disk  with  openings  arranged  properly  in  steps. 

Many  demonstrations  of  the  chief  illusion  of 
brightness-contrast  are  visible  at  night  under  glaring 
lighting  conditions.  It  is  difficult  or  impossible  to  see 
objects  beyond  automobile  headlights,  and  adjacent 
to  them,  in  the  visual  field.  Objects  similarly  located 
in  respect  to  any  surface  sufficiently  bright  are  more 
or  less  obscured.  Characters  written  upon  a  black- 
board, placed  between  two  windows,  may  be  invisible 
if  the  surfaces  seen  through  the  window  are  quite 
bright,  unless  a  sufficient  quantity  of  light  reaches  the 
blackboard  from  other  sources.  Stage-settings  have 


120  VISUAL  ILLUSIONS 

been  changed  in  perfect  obscurity  before  an  audience 
by  turning  on  a  row  of  bright  lights  at  the  edge  of 
the  stage-opening.  The  term  "  blinding  light  "  owes 
its  origin  to  this  effect  of  brightness-contrast. 

The  line  of  juncture  between  a  bright  and  a  dark 
surface  may  not  be  seen  as  a  sharp  line,  but  as  a 
narrow  band  of  gray.  When  this  is  true  it  is  possible 
that  an  undue  amount  of  area  is  credited  to  the  white. 
In  preceding  paragraphs  we  have  seen  the  peculiar 
effect  at  the  border-lines  of  a  series  of  grays.  This 
may  have  something  to  do  with  the  estimate;  how- 
ever, irradiation  may  be  due  to  excitation  of  retinal 
rods  and  cones  adjacent  to,  but  not  actually  within 
the  bright  image. 

A  remarkable  effect  which  may  be  partially  attrib- 
utable to  irradiation  can  be  produced  by  crossing  a 
grating  of  parallel  black  lines  with  an  oblique  black 
line.  At  the  actual  crossings  the  black  appears  to  run 
up  the  narrow  angle  somewhat  like  ink  would  under 
the  influence  of  surface  tension.  This  is  particularly 
striking  when  two  gratings  or  even  two  ordinary  fly- 
screens  are  superposed.  The  effect  is  visible  when 
passing  two  picket-fences,  one  beyond  the  other.  If 
a  dark  object  is  held  so  that  a  straight  edge  appears 
to  cross  a  candle-flame  or  other  light-source,  at  this 
portion  the  straight  edge  will  appear  to  have  a  notch 
in  it. 

Irradiation  in  general  has  been  defined  as  the 
lateral  diffusion  of  nervous  stimuli  beyond  the  actual 
stimulus.  It  is  not  confined  to  the  visual  sense  but 
irradiation  for  this  sense  is  a  term  applied  to  the 
apparent  enlargement  of  bright  surfaces  at  the  ex- 


IRRADIATION  AND  BRIGHTNESS  -  CONTRAST      121 

pense  of  adjacent  darker  surfaces.  The  crescent  of 
the  new  moon  appears  larger  in  radius  than  the  faint 
outline  of  the  darker  portion  which  is  feebly  illumi- 
nated chiefly  by  light  reflected  from  the  earth's  surface. 
A  filament  of  a  lamp  appears  to  grow  in  size  as  the 
current  through  it  is  slowly  increased  from  a  zero 
value;  that  is,  as  it  increases  in  brightness.  In  Fig.  65 


Fig.  65.  —  The  phenomenon  of  irradiation. 

the  small  inner  squares  are  of  the  same  size  but  the 
white  square  appears  larger  than  the  black  one.  It 
seems  that  this  apparent  increase  is  made  at  the  ex- 
pense of  the  adjacent  dark  area.  This  phenomenon 
or  illusion  is  strongest  when  the  brightness  is  most 
intense,  and  is  said  to  be  greatest  when  the  accommo- 
dation is  imperfect.  A  very  intense  light-source  may 
appear  many  times  larger  than  its  actual  physical 
size. 

Doubtless  a  number  of  factors  may  play  a  part  in 
this  phenomenon.  It  appears  possible  that  there  is  a 
rapid  spreading  of  the  excitation  over  the  retina  ex- 


122  VISUAL  ILLUSIONS 

tending  quite  beyond  the  border  of  the  more  intensely 
stimulated  region,  but  this  must  be  practically  in- 
stantaneous in  order  to  satisfy  results  of  experiments. 
Eye-movements  may  play  some  part  for,  despite  the 
most  serious  efforts  to  fixate  the  point  of  sight,  a 
fringe  will  appear  on  the  borders  of  images  which  is 
certainly  due  to  involuntary  eye-movements. 

Irradiation  has  also  been  ascribed  to  spherical 
aberration  in  the  eye-lens  and  to  diffraction  of  light 
at  the  pupil.  Printed  type  appears  considerably  re- 
duced in  size  when  the  pupil  is  dilated  with  atropin 
and  is  restored  to  normal  appearance  when  a  small 
artificial  pupil  is  placed  before  the  dilated  pupil.  It 
has  been  suggested  that  chromatic  aberration  in  the 
eye-lens  is  a  contributory  cause,  but  this  cannot  be 
very  important,  for  the  illusion  is  visible  with  mono- 
chromatic light  which  eliminates  chromatic  aberration. 
The  experimental  evidence  appears  to  indicate  that 
the  phenomenon  is  of  a  physical  nature. 

There  are  variations  in  the  effects  attributable  to 
radiation,  and  it  is  difficult  to  reduce  them  to  simple 
terms.  Perhaps  it  may  aid  the  reader  [to  have  before 
him  the  classification  presented  by  Boswell.4  He 
describes  the  varieties  of  irradiation  as  follows: 

1.  Very  rapid  spreading  of  the  excitation  over  the  retina 
extending  far  beyond  the  border  of  the  stimulated  region  and 
occurring  immediately  upon  impact  of  the  stimulating  light. 

2.  Irradiation  within  the   stimulated  portion  of  the  retina 
after  the  form  of  a  figure  becomes  distinctly  perceptible. 

3.  Emanations   of   decreasing   intensity   extend   themselves 
outward  and  backward  from  a  moving  image  until  lost  in  the 
darkness  of  the  background. 

4.  A  well  known  form  of  irradiation  which  occurs  when  a 


IRRADIATION  AND  BRIGHTNESS  -  CONTRAST      123 

surface  of  greater  intensity  enlarges  itself  at  the  expense  of 
one  of  less  intensity. 

5.  A  form  having  many  of  the  characteristics  of  the  first 
type,  but  occurring  only  after  long  periods  of  stimulation,  of  the 
magnitude  of  30  to  60  seconds  or  more. 


IX 
COLOR 

IN  order  to  simplify  the  presentation  of  the  general 
subject,  discussions  of  color  have  been  omitted  in 

so  far  as  possible  from  the  preceding  chapters. 
There  are  almost  numberless  phenomena  involving 
color,  many  of  which  are  illusions,  or  seemingly  so. 
It  will  be  obvious  that  many  are  errors  of  sense; 
some  are  errors  of  judgment;  others  are  errors  due 
to  defects  of  the  optical  system  of  the  eye ;  and  many 
may  be  ascribed  to  certain  characteristics  of  the  visual 
process.  It  is  not  the  intention  to  cover  the  entire 
field  in  detail;  indeed,  this  could  not  be  done  within 
the  confines  of  a  large  volume.  However,  substantial 
glimpses  of  the  more  important  phases  of  color  as 
related  to  illusions  are  presented  in  this  chapter.  In 
the  early  chapters  pertaining  to  the  eye  and  to  vision 
some  of  the  following  points  were  necessarily  touched 
upon,  but  the  repetition  in  the  paragraphs  which 
follow  is  avoided  as  much  as  possible. 

Simultaneous  Contrast  —  That  the  life  of  color  is 
due  to  contrast  is  demonstrable  in  many  ways.  If  a 
room  is  illuminated  by  deep  red  light,  at  first  this 
color  is  very  vivid  in  consciousness ;  however,  gradu- 
ally it  becomes  less  saturated.  After  a  half  hour  the 
color  is  apparently  a  much  faded  red  but  upon  emerg- 
ing from  the  room  into  one  normally  lighted,  the 

124 


COLOR  125 


latter  appears  very  markedly  greenish  in  tint.  The 
reason  that  the  pure  red  light  does  not  appear  as 
strongly  colored  as  it  really  is,  is  due  to  the  lack  of 
contrast.  In  a  similar  manner  at  night  we  see  white 
objects  as  white  even  under  the  yellowish  artificial 
light.  The  latter  appears  very  yellow  in  color  when 
it  is  first  turned  on  as  daylight  wanes  but  as  darkness 
falls  and  time  elapses  it  gradually  assumes  a  colorless 
appearance. 

An  apparatus  constructed  after  the  plan  of  Fig.  62 
is  very  effective  for  demonstrating  the  remarkable 
effects  of  color-contrast  but  some  additions  will  add 
considerably  to  its  convenience.  If  the  lamps  F  are 
divided  into  three  circuits,  each  emitting,  respectively, 
red,  green,  and  blue  primary  colors,  it  is  possible  by 
means  of  controlling  rheostats  to  illuminate  E,  the 
environment,  with  light  of  any  hue  (including  purple), 
of  any  saturation,  and  of  a  wide  range  of  intensities 
or  resulting  brightnesses.  Thus  we  have  a  very 
simple  apparatus  for  quickly  providing  almost  number- 
less environments  for  H.  The  same  scheme  can  be 
applied  to  lamps  /?,  with  the  result  that  a  vast  array 
of  colors  may  be  seen  through  the  hole  H.  If  the 
hole  is  the  shape  of  the  star  in  Fig.  66  it  will  be  found 
very  effective.  The  observer  will  actually  see  a  star 
of  any  desired  color  amid  an  environment  of  any 
desired  color.  Care  should  be  taken  to  have  the 
star  cut  in  very  thin  material  in  order  to  eliminate 
conspicuous  boundary  lines.  It  is  quite  satisfactory 
to  use  a  series  of  colored  papers  on  a  slide  at  C  and 
ordinary  clear  lamps  at  R.  By  means  of  this  apparatus 
both  contrasts  —  hue  and  brightness  —  may  be  dem- 


126  VISUAL  ILLUSIONS 

onstrated.  Of  course,  for  black  and  white  only  bright- 
ness-contrast is  present;  but  in  general  where  there 
is  color-contrast  there  is  also  brightness-contrast. 
The  latter  may  be  reduced  or  even  eliminated  if  the 
brightness  of  the  star  and  of  its  surroundings  are 
made  equal,  but  it  is  difficult  to  make  a  satisfactory 
balance  in  this  respect.  Assuming,  however,  that 
brightness-contrast  is  eliminated,  we  have  left  only 


Fig.  66.  —  An  excellent  pattern  for  demon- 
strating color-contrast. 

hue  and  saturation  contrast,  or  what  will  be  termed 
(rather  loosely,  it  is  admitted)  color-contrast. 

If  the  surroundings  are  dark  and,  for  example,  an 
orange  star  is  seen  alone,  it  does  not  appear  very 
colorful.  However,  if  the  surroundings  are  now  made 
bright  with  white  light,  the  star  appears  quite  satu- 
rated. With  blue  or  green  light  the  orange  star  ap- 
pears even  more  intensely  orange,  but  when  the  color- 
contrast  is  reduced,  as  in  the  case  of  yellow  or  red 
surroundings,  the  vividness  of  the  orange  star  again 
decreases.  This  may  be  summarized  by  stating  that 


COLOR  127 


two  widely  different  colors  viewed  in  this  manner  will 
mutually  affect  each  other  so  that  they  appear  still 
more  different  in  hue.  If  their  hues  are  close  to- 
gether spectrally  this  effect  is  not  as  apparent.  For 
example,  if  orange  and  green  are  contrasted,  the 
orange  will  appear  reddish  in  hue  and  the  green  will 
appear  bluish. 

Let  us  now  assume  the  star  to  be  white,  and  that 
the  surroundings  are  of  any  color  of  approximately 
the  same  brightness.  The  star  which  is  really  white 
will  now  appear  decidedly  tinted  and  of  a  hue  ap- 
proximately complementary  to  that  of  the  surround- 
ings. When  the  latter  are  of  a  green  color  the  white 
star  will  assume  a  purplish  tinge ;  when  red  the  white 
star  will  appear  of  a  blue-green  tint;  when  yellow 
the  white  star  will  appear  bluish.  This  is  an  illusion 
in  any  sense  of  the  term. 

The  strength  of  this  illusion  caused  by  simul- 
taneous contrast  is  very  remarkable.  For  example, 
if  a  grayish  purple  star  is  viewed  amid  intense  green 
surroundings  it  will  appear  richly  purple,  but  when  the 
surroundings  are  changed  to  a  rich  purple  the  gray- 
ish purple  star  will  even  appear  greenish.  The  ap- 
parent change  of  a  color  to  its  complementary  by 
merely  altering  its  environment  is  really  a  remarkable 
illusion. 

The  importance  of  simultaneous  contrast  is  easily 
demonstrated  upon  a  painting  by  isolating  any  colored 
object  from  its  surroundings  by  means  of  a  hole  in  a 
gray  card.  For  example,  an  orange  flower-pot  amid 
the  green  foliage  of  its  surroundings  will  appear 
decidedly  different  in  color  and  brightness  than  when 


128  VISUAL  ILLUSIONS 

viewed  through  a  hole  in  a  white,  black,  or  gray  card- 
board. By  means  of  colored  papers  the  same  color 
may  be  placed  in  many  different  environments  and 
the  various  contrasts  may  be  viewed  simultaneously. 
The  extent  of  the  illusion  is  very  evident  when  re- 
vealed in  this  simple  manner.  However,  too  much 
emphasis  cannot  be  given  to  Figs.  62  and  66  as  a 
powerful  means  for  realizing  the  greatest  effects. 

After-images.  —  After  looking  at  bright  objects  we 
see  after-images  of  the  same  size  and  form  which 
vary  more  or  less  in  color.  These  after-images_are 
due  to  persistence  or  fatigue  of  the  visual  process, 
depending  upon  conditions.  After  looking  at  the  sun 
for  a  moment  a  very  bright  after-image  is  seen.  Un- 
doubtedly this  at  first  is  due  to  a  persistence  of  the 
visual  process,  but  as  it  decays  it  continuously  changes 
color  and  finally  its  presence  is  due  to  fatigue. 

After-images  may  be  seen  after  looking  intently 
at  any  object  and  then  directing  the  eyes  toward  a 
blank  surface  such  as  a  wall.  A  picture-frame  will  be 
seen  as  a  rectangular  after-image;  a  checkered 
pattern  will  be  seen  as  a  checkered  after-image. 
When  these  after-images  are  projected  upon  other 
objects  it  is  obvious  that  the  appearance  of  the  latter 
is  apparently  altered  especially  when  the  observer  is 
not  conscious  of  the  after-image.  The  effects  are 
seen  in  paintings  and  many  peculiar  phenomena  in 
the  various  arts  are  directly  traceable  to  after-imgaes. 

It  appears  unnecessary  to  detail  the  many  effects 
for  the  explanations  or  at  least  the  general  principles 
of  after-images  are  so  simple  that  the  reader  should 
easily  render  an  analysis  of  any  given  case. 


COLOR  129 


Let  us  assume  that  vision  is  fixed  upon  a  green 
square  upon  a  gray  or  white  background.  Despite 
the  utmost  effort  on  the  part  of  the  observer  to  gaze 
fixedly  upon  this  green  square,  the  latter  will  begin 
to  appear  fringed  with  a  pinkish  border.  This  is  due 
to  the  after-image  of  the  green  square  and  it  is  dis- 
placed slightly  due  to  involuntary  eye-movements. 
After  gazing  as  steadily  as  possible  for  a  half 
minute,  or  even  less,  if  the  point  of  sight  is  turned 
to  the  white  paper  a  pink  square  is  seen  upon  it. 
Furthermore,  this  pink  square  moves  over  the  field 
with  the  point  of  sight.  This  is  the  type  most  gen- 
erally noticed. 

After-images  have  been  classified  as  positive  and 
negative.  The  former  are  those  in  which  the  distri- 
bution of  light  and  shade  is  the  same  as  in  the  origi- 
nal object.  Those  in  which  this  distribution  is  re- 
versed, as  in  the  photographic  negative,  are  termed 
"  negative."  After-images  undergo  a  variety  of 
changes  in  color  but  in  general  there  are  two  im- 
portant states.  In  one  the  color  is  the  same  as  in  the 
original  object  and  in  the  other  it  is  approximately 
complementary  to  the  original  color.  In  general  the 
negative  after-image  is  approximately  complementary 
in  color  to  the  color  of  the  original  object. 

After-images  are  best  observed  when  the  eyes  are 
well  rested,  as  in  the  morning  upon  awakening.  With 
a  little  practice  in  giving  attention  to  them,  they  can 
be  seen  floating  in  the  air,  in  the  indefinite  field  of  the 
closed  eyes,  upon  a  wall,  or  elsewhere,  and  the  changes 
in  the  brightness  and  color  can  be  readily  followed. 
Negative  after-images  are  sometimes  very  persistent 


130  VISUAL  ILLUSIONS 

and  therefore  are  more  commonly  noticed  than  posi- 
tive ones.  The  positive  after-image  is  due  to  retinal 
inertia,  that  is,  to  the  persistency  of  the  visual  process 
after  the  actual  stimulus  has  been  removed.  It  is  of 
relatively  brief  duration.  If  an  after-image  of  a  window 
is  projected  on  a  white  area  it  is  likely  to  appear  as  a 
v.  "  negative  "  when  projected  upon  a  white  background, 
and  as  a  "  positive  "  upon  a  dark  background,  such  as  is 
readily  provided  by  closing  the  eyes.  It  may  be  of 
interest  for  the  reader  to  obtain  an  after-image  of  a 
bright  surface  of  a  light-source  and  study  its  color 
changes  with  the  eye  closed.  Upon  repeating  the 
experiment  the  progression  of  colors  will  be  found 
to  be  always  the  same  for  the  same  conditions. 
The  duration  of  the  after-image  will  be  found  to 
vary  with  the  brightness  and  period  of  fixation  of  [the 
object. 

It  is  interesting  to  note  that  an  after-image  is  seen 
with  difficulty  when  the  eyes  are  in  motion,  but  it 
becomes  quite  conspicuous  when  the  eyes  are  brought 
to  rest. 

An  after-image  due  to  the  stimulation  of  only  one 
eye  sometimes  seems  to  be  seen  by  the  other  eye. 
Naturally  this  has  given  rise  to  the  suggestion  that 
the  seat  of  after-images  is  central  rather  than  pe- 
ripheral; that  is,  in  the  brain  rather  than  at  the  ret- 
ina. However,  this  is  not  generally  the  case  and  the 
experimental  evidence  weighs  heavily  against  this 
conclusion. 

If  Fig.  52  is  revolved  about  its  center  and  fixated 
for  some  time  striking  effects  are  obtained  upon  look- 
ing away  suddenly  upon  any  object.  The  latter  will 


COLOR  131 


appear  to  shrink  if  the  spiral  has  seemed  to  run 
outward,  or  to  expand  if  the  spiral  has  seemed 
to  run  inward.  These  are  clearly  after-images  of 
motion. 

As  stated  elsewhere,  we  may  have  illusions  of 
after-images  as  well  as  of  the  original  images.  For 
example,  if  a  clearly  defined  plane  geometrical  figure 
such  as  a  cross  or  square  is  bright  enough  to  produce 
a  strong  after-image,  the  latter  when  projected  upon 
a  perspective  drawing  will  appear  distorted;  that  is, 
it  is  likely  to  appear  hi  perspective. 

A  simple  way  of  demonstrating  after-images  and 
their  duration  is  to  move  the  object  producing  them. 
For  example,  extinguish  a  match  and  move  the  glow- 
ing end.  If  observed  carefully  without  moving  the 
eye  a  bluish  after-image  will  be  seen  to  follow  the 
glowing  end  of  the  match.  In  this  case  the  eyes  should 
be  directed  straight  ahead  while  the  stimulus  is  moving 
and  the  observation  must  be  made  by  averted  or  in- 
direct vision. 

Growth  and  Decay  of  Sensation.  —  Although  many 
after-images  may  not  be  considered  to  be  illusions 
in  the  sense  in  which  the  term  is  used  here,  there 
are  many  illusions  hi  which  they  at  least  play  a  part. 
Furthermore,   it   is   the   intention   throughout   these 
chapters  to  adhere  to  a  discussion  of  "  static  "  il- 
lusions, it  is  difficult  to  avoid  touching  occasionally 
upon  motion.    The  eyes  are  in  motion  most  of  the  I 
time,  hence,  certain  effects  of  an  illusory  nature  may  i 
be  superposed  upon  stationary  objects. 

The  persistence  of  vision  has  been  demonstrated 
by  every  small  boy  as  he  waved  a  glowing  stick  seized 


132  VISUAL  ILLUSIONS 

from  a  bonfire.  Fireworks  owe  much  of  their  beauty 
to  this  phenomenon.  A  rapidly  revolving  spoked 
wheel  may  appear  to  be  a  more  or  less  transparent 
disk,  but  occasionally  when  a  rapid  eye-movement 
moves  the  point  of  sight  with  sufficient  speed  in  the 
direction  of  motion,  the  spokes  reappear  momentarily. 
Motion-pictures  owe  their  success  to  this  visual  prop- 
erty—  the  persistence  of  vision.  If  a  lantern-slide 
picture  be  focused  upon  black  velvet  or  upon  a  dark 
doorway,  the  projected  image  will  not  be  seen.  How- 
ever, if  a  white  rod  be  moved  rapidly  enough  in  the 
plane  of  the  image,  the  latter  may  be  seen  in  its  en- 
tirety. The  mixture  of  colors,  by  rotating  them  on 
disks,  owes  its  possibility  to  the  persistence  of  the 
color-sensations  beyond  the  period  of  actual  stimu- 
lation. The  fact  that  it  takes  time  for  sensations  of 
light  to  grow  and  decay  is  not  as  important  here  as 
the  fact  that  the  rates  of  growth,  and  also  of  decay, 
vary  for  different  colors.  In  general,  the  growth  and 
the  decay  are  not  of  similar  or  uniform  rates.  Further- 
more, the  sensation  often  initially  "  overshoots  "  its 
final  steady  value,  the  amount  of  "  overshooting " 
depending  upon  the  intensity  and  color  of  the  stimulus. 
These  effects  may  be  witnessed  in  their  extensive 
variety  by  rotating  disks  so  constructed  that  black 
and  various  colors  stimulate  the  retina  in  definite 
orders. 

An  interesting  case  of  this  kind  may  be  demon- 
strated by  rotating  the  disk  shown  in  Fig.  67.  Not- 
withstanding the  fact  that  these  are  only  black  and 
white  stimuli,  a  series  of  colored  rings  is  seen  varying 
from  a  reddish  chocolate  to  a  blue-green.  Experiment 


COLOR  133 


will  determine  the  best  speed,  which  is  rather  slow 
under  a  moderate  intensity  of  illumination.  The 
reddish  rings  will  be  outermost  and  the  blue-green 
rings  innermost  when  the  disk  is  rotated  in  one  di- 
rection. Upon  reversing  the  direction  of  rotation  the 
positions  of  these  colored  rings  will  be  reversed.  By 


Fig.  67.  —  By  rotating  this  Mason  (black  and 
white)  disk  color-sensations  are  produced. 

using  various  colors,  such  as  red  and  green  for  the 
white  and  black  respectively,  other  colors  will  be 
produced,  some  of  which  are  very  striking.  The 
complete  explanation  of  the  phenomenon  is  not  clear, 
owing  to  the  doubt  which  exists  concerning  many  of 
the  phenomena  of  color-vision,  but  it  appears  certain 
that  the  difference  in  the  rates  of  growth  and  decay 
of  the  various  color-sensations  (the  white  stimulus 
includes  all  the  spectral  hues  of  the  illuminant)  is  at 
least  partially,  if  not  wholly,  responsible. 


134  VISUAL  ILLUSIONS 

An  interesting  effect,  perhaps  due  wholly  or  in 
part  to  the  differences  in  the  rates  of  growth  and  decay 
of  color-sensations,  may  be  observed  when  a  colored 
pattern  is  moved  under  a  low  intensity  of  illumination, 
the  eyes  remaining  focused  upon  a  point  in  space  at 
about  the  same  distance  as  the  object.  A  square  of 
red  paper  pasted  in  the  center  of  a  larger  piece  of 
blue-green  paper  is  a  satisfactory  object.  On  moving 
this  object  gently,  keeping  the  point  of  sight  fixed  in 
its  plane  of  movement,  the  central  red  square  will 
appear  to  shake  like  jelly  and  a  decided  trail  of  color 
will  appear  to  cling  to  the  lagging  edge  of  the  central 
square.  Perhaps  chromatic  aberration  plays  some 
part  in  making  this  effect  so  conspicuous. 

A  similar  case  will  be  noted  in  a  photographic 
dark-room  illuminated  by  red  light  upon  observing 
the  self-luminous  dial  of  a  watch  or  clock.  When 
the  latter  is  moved  in  the  plane  of  the  dial,  the  greenish 
luminous  figures  appear  separated  from  the  red  dial 
and  seem  to  lag  behind  during  the  movement.  For 
such  demonstrations  it  is  well  to  experiment  some- 
what by  varying  the  intensity  of  the  illumination  and 
the  speed  of  movement.  Relatively  low  values  of 
each  appear  to  be  best. 

Although  the  various  color-sensations  grow  and 
decay  at  different  rates,  the  latter  depend  upon  con- 
ditions. It  appears  that  blue-sensation  rises  very 
rapidly  and  greatly  overshoots  its  final  steady  value 
for  a  given  stimulus.  Red  ranks  next  and  green  third 
in  this  respect.  The  overshooting  appears  to  be  greater 
for  the  greater  intensity  of  the  stimulus.  The  time 
required  for  the  sensation  to  reach  a  steady  value 


COLOR  135 


depends  both  upon  the  spectral  character  and  the 
brightness  of  the  color  but  is  usually  less  than  a 
second. 

Chromatic  Aberration.  —  It  is  well  known  that 
the  eye  focuses  different  spectral  colors  at  different 
points.  This  is  true  of  any  simple  lens  and  the  defect 
is  overcome  in  the  manufacture  of  optical  instruments 
by  combining  two  lenses  consisting  respectively  of 
glasses  differing  considerably  in  refractive  index.  If 
a  white  object  is  viewed  by  the  eye,  it  should  appear 
with  a  purplish  fringe ;  however,  the  effect  is  observed 
more  readily  by  viewing  a  light-source  through  a 
purple  filter  which  transmits  only  violet  and  red  light. 
The  light-source  will  have  a  red  or  a  violet  fringe, 
depending  upon  the  accommodation  or  focus  of  the 
eye. 

This  effect  is  perhaps  best  witnessed  on  viewing 
a  line  spectrum  such  as  that  of  the  mercury  arc,  focused 
upon  a  ground  glass.  The  violet  and  blue  lines  are 
not  seen  in  good  focus  when  the  eyes  are  focused 
upon  the  green  and  yellow  lines.  Furthermore,  the 
former  can  be  seen  in  excellent  focus  at  a  distance  too 
short  for  accommodating  the  eyes  to  the  green  and  the 
yellow  lines.  This  experiment  shows  that  the  focal 
length  of  the  optical  system  of  the  eye  is  considerably 
shorter  for  the  spectral  hues  of  shorter  wave-length 
(violet,  blue)  than  for  those  of  longer  wave-length 
(such  as  yellow).  Narrow  slits  covered  with  diffusing 
glass  and  illuminated  respectively  by  fairly  pure  blue, 
green,  yellow,  and  red  lights  may  be  substituted. 

The  effect  may  be  demonstrated  by  trying  to  focus 
fine  detail  such  as  print  when  two  adjacent  areas  are 


136  VISUAL  ILLUSIONS 

illuminated  by  blue  and  red  lights  respectively.  It  is 
also  observed  when  fine  detail  such  as  black  lines 
are  held  close  to  the  eye  for  colored  fringes  are  seen. 
This  optical  defect  is  responsible  for  certain  visual 
illusions. 

An  excellent  demonstration  of  chromatic  aber- 
ration in  the  eye  is  found  by  viewing  fine  detail 
through  a  purple  filter.  Now  if  a  red  filter  be  super- 
posed on  the  purple  one  only  the  red  light  is  trans- 
mitted. Notwithstanding  the  decrease  in  illumination 
or  rather  of  light  reaching  the  eye,  measurement 
shows  that  finer  detail  can  be  discriminated  than  in 
the  first  case.  A  similar  result  is  found  on  super- 
posing a  blue  filter  upon  the  purple  one. 

Retiring  and  Advancing  Colors.  —  For  years  the 
artist  and  the  decorator  have  felt  that  certain  colors 
seem  to  advance  nearer  than  others  or  that  the  latter 
seem  to  retire  more  than  the  former.  The  author  5 
obtained  actual  measurements  of  this  phenomenon, 
but  the  evidence  also  indicated  that  the  effects  were 
not  the  same  for  all  persons.  The  phenomenon  is 
very  noticeable  in  the  case  of  the  image  of  a  colored 
lantern-slide  projected  upon  a  screen  and  is  readily 
observed  when  the  image  consists  of  letters  of  various 
colors.  In  the  case  of  red  and  green  letters,  for  ex- 
ample, the  former  appear  (to  most  persons)  to  be 
considerably  nearer  the  observer  than  the  green 
letters.  It  has  appeared  to  the  writer  that  the  illusion 
is  apparent  even  for  white  letters  upon  a  dark  back- 
ground. In  general,  the  colors  whose  dominant  hues 
are  of  the  shorter  wave-lengths  (violet,  blue,  blue- 
green,  green)  are  retiring  and  those  whose  dominant 


COLOR 


137 


'hues  are  of  the  longer  wave-lengths  (yellow,  orange, 
red)  are  advancing. 

In  order  to  obtain  experimental  measurements 
two  light-tight  boxes,  each  containing  a  light-source, 
were  arranged  to  run  independently  upon  tracks. 
Over  the  front  end  of  each  a  diaphragm  was  placed 
so  that  the  observer  saw  two  characters  as  in  Fig.  68. 
A  saturated  red  filter  was  placed  over  one  and  a 
saturated  blue  filter  over  the  other.  In  a  dark  room 


U 
Jl 


Fig.  68.  —  For  demonstrating  retiring  and  advancing  colors. 

the  observer  saw  a  blue  E  and  a  red  H  standing  out 
in  the  darkness.  One  of  these  boxes  was  fastened  so 
as  to  be  immovable  and  the  observer  moved  the  other 
to  and  fro  by  means  of  a  cord  over  pulleys  until  the 
two  characters  appeared  equi-distant  from  him.  This 
was  done  for  a  series  of  distances  of  the  stationary 
box  from  the  observer's  eye.  Nearly  all  the  observers 
(without  being  acquainted  with  the  positions)  were 
obliged  to  set  the  red  H  further  behind  the  blue  E 
in  order  that  both  appeared  at  the  same  distance. 
This  added  distance  for  the  red  H  was  as  much  as 
2.4  feet  when  the  blue  E  was  at  a  distance  of  24  feet. 
In  other  words  the  difference  in  the  positions  of  the 


138  VISUAL  ILLUSIONS 

two  was  as  much  as  10  per  cent  of  the  total  distance 
in  this  case. 

Many  other  interesting  data  were  obtained  but 
most  of  these  are  not  particularly  of  interest  here. 
Some  of  the  experiments  tended  to  show  the  effect 
of  certain  optical  defects  in  the  eye  and  the  variations 
and  even  reversal  of  the  effect  for  some  persons  were 
accounted  for  by  differences  in  the  curvatures,  etc., 
of  certain  eye-media  for  the  observers.  These  details 
are  not  of  interest  here  but  it  may  be  of  interest  to 
know  that  the  phenomenon  may  be  accounted  for  by 
the  chromatic  aberration  in  the  eye.  This  may  not 
be  the  true  explanation,  or  it  may  be  only  partially 
correct.  Perhaps  some  of  the  illusion  is  purely  psycho- 
logical in  origin.  Certainly  the  illusion  is  very  ap- 
parent to  most  careful  observers. 

Color-sensibility  of  the  Retina.  \ —  This  aspect  was 
touched  upon  in  Chapter  III,  but  the  differences  in 
the  sensibility  of  various  areas  of  the  retina  to  various 
colors  are  of  sufficient  importance  to  be  discussed 
further.  The  ability  to  distinguish  light  and  color 
gradually  fades  or  decreases  at  the  periphery  of  the 
visual  field,  but  the  actual  areas  of  the  fields  of  per- 
ception vary  considerably,  depending  upon  the  hue  or 
spectral  character  of  the  light  reaching  the  retina. 
The  extreme  peripheral  region  of  the  visual  field  is 
"color-blind";  that  is,  color  ceases  to  be  perceived 
before  brightness-perception  vanishes  in  the  out- 
skirts of  the  visual  field.  These  fields  for  various 
colors  depend  in  size  and  contour  not  only  upon  the 
hue  or  spectral  character  of  the  light-stimuli  but  also 
upon  the  intensity  and  perhaps  upon  the  size  of  the 


COLOR  139 


stimuli.  There  is  some  disagreement  as  to  the  rela- 
tive sizes  of  these  fields  but  it  appears  that  they  in- 
crease in  size  in  the  following  order:  green,  red,  blue, 
white  (colorless).  The  performances  of  after-images, 
and  the  rates  of  growth  and  decay  of  sensation  vary 
for  different  colors  and  for  different  areas  of  the  retina, 
but  it  would  be  tedious  to  peruse  the  many  details  of 
these  aspects  of  vision.  They  are  mentioned  in 
order  that  the  reader  may  take  them  into  account 
in  any  specific  case. 

As  already  stated,  the  central  part  of  the  visual 
field  —  the  fovea  upon  which  we  depend  for  acute 
vision  —  contains  a  yellowish  pigmentation,  which  is 
responsible  for  the  term  "  yellow  spot."  This  oper- 
ates as  a  yellow  filter  for  this  central  area  and  modifies 
the  appearance  of  visual  fields  quite  the  same  as  if  a 
similar  yellow  filter  was  placed  in  the  central  position 
of  the  field  of  vision.  The  effect  of  the  selectivity 
of  the  "  yellow  spot  "  is  noticeable  in  viewing  certain 
colors. 

Purkinje  Effect.  —  The  relative  sensibility  of  the 
retina  varies  for  different  colors  with  a  change  in 
brightness ;  or  it  may  be  better  to  state  that  the  rela- 
tive sensations  for  various  colors  alters  as  the  bright- 
ness values  are  reduced  to  a  low  intensity.  For  ex- 
ample, if  a  reddish  purple  (consisting  of  red  and  blue 
or  violet  rays)  be  illuminated  in  such  a  manner  that 
the  intensity  of  illumination,  and  consequently  its 
brightness,  may  be  reduced  from  normal  to  a  low 
value  (approximating  moonlight  conditions),  it  will  be 
seen  to  vary  from  reddish  purple  to  violet.  In  doing 
this  its  appearance  changes  through  the  range  of 


140  VISUAL  ILLUSIONS 

purples  from  reddish  to  violet.  This  can  be  ac- 
complished by  orientation  of  the  purple  surface 
throughout  various  angles  with  respect  to  the  di- 
rection of  light  or  by  reducing  the  illumination  by 
means  of  screens. 

In  general  the  Purkinje  effect  may  be  described 
as  an  increasing  sensibility  of  the  retina  for  light  of 
shorter  wave-lengths  (violet,  blue,  green)  as  the 
brightness  decreases,  or  a  corresponding  decreasing 
sensibility  for  light  of  longer  wave-lengths  (yellow, 
orange,  red).  The  effect  may  be  seen  on  any  colored 
surfaces  at  twilight  illumination.  A  blue  and  a  red 
flower,  which  appear  of  the  same  brightness  before 
sunset  will  begin  to  appear  unequal  in  this  respect 
as  twilight  deepens.  The  red  will  become  darker 
more  rapidly  than  the  blue  if  there  are  no  appreciable 
changes  in  the  color  of  the  daylight.  Finally  all  color 
disappears.  It  is  better  to  perform  this  experiment 
under  artificial  light,  in  order  that  the  spectral  charac- 
ter of  the  illuminant  may  be  certain  to  remain  con- 
stant. In  this  case  rheostats  must  not  be  used  for 
dimming  the  light  because  of  the  attendant  changes 
in  color  or  quality  of  the  light. 

The  Purkinje  effect  may  be  noticed  by  the  careful 
observer  and  it  is*  responsible  for  certain  illusions. 
Apparently  it  cannot  operate  over  one  portion  of  the 
retina,  while  the  remainder  is  stimulated  by  normal 
intensities  of  light. 

Retinal  Rivalry.  —  Many  curious  effects  may  be 
obtained  by  stimulating  the  two  retinas  with  lights 
respectively  different  in  color.  For  example,  it  is 
interesting  to  place  a  blue  glass  before  one  eye  and  a 


COLOR  141 


yellow  or  red  one  before  the  other.  The  two  inde- 
pendent monocular  fields  strive  for  supremacy  and 
this  rivalry  is  quite  impressive.  For  a  moment  the 
whole  field  may  appear  of  one  color  and  then  suddenly 
it  will  appear  of  the  other  color.  Apparently  the 
fluctuation  of  attention  is  a  factor.  Usually  it  does 
not  seem  to  be  possible  to  reach  a  quiescent  state  or 
a  perfect  mixture  of  the  two  colors  in  this  manner. 
The  dependence  of  one  monocular  field  upon  the 


Pig.  69.  —  By  combining  these  stereoscopically  the  effect  of  metallic 
lustre  (similar  to  graphite  in  this  case)  is  obtained. 


other,  and  also  their  independence,  are  emphasized 
by  this  experiment.  It  is  of  interest  to  consider  the 
illusions  of  reversible  perspective  and  others  in 
Chapter  V  in  this  connection. 

One  of  the  interesting  results  of  retinal  rivalry  is 
found  in  combining  two  stereoscopic  pictures  in  black 
and  white  with  the  black  and  white  reversed  in  one 
of  them.  The  apparently  solid  object  will  appear  to 
possess  lustre.  The  experiment  may  be  tried  with 
Fig.  69  by  combining  the  two  stereoscopic  pictures  by 
converging  or  diverging  the  axes  of  the  eyes  as  de- 
scribed in  connection  with  Figs.  2  and  3. 

It  will  be  noted  that  in  order  for  two  stereoscopic 
pictures,  when  combined,  to  produce  a  perfect  effect 


142  VISUAL  ILLUSIONS 

of  three  dimensions  their  dissimilarity  must  be  no 
more  than  that  existing  between  the  two  views  from 
the  two  eyes  respectively.  The  dissimilarity  in  Fig.  69 
is  correct  as  to  perspective,  but  the  reversal  of  white 
and  black  in  one  of  them  produces  an  effect  beyond 
that  of  true  third  dimension.  When  the  colors  are  so 
arranged  in  such  pictures  as  to  be  quite  different  in 
the  two  the  effects  are  striking.  There  is,  in  such 
cases,  an  effect  beyond  that  of  perfect  binocular 
combination. 

By  means  of  the  stereoscope  it  is  possible  to  attain 
binocular  mixture  of  colors  but  this  is  usually  difficult 
to  accomplish.  The  difficulty  decreases  as  the  bright- 
ness and  saturation  of  the  colors  decrease  and  is  less 
for  colors  which  do  not  differ  much  in  hue  and  in 
brightness.  These  effects  may  be  studied  at  any 
moment,  for  it  is  only  necessary  to  throw  the  eyes 
out  of  focus  for  any  object  and  to  note  the  results. 
Many  simple  experiments  may  be  arranged  for  a 
stereoscope,  using  black  and  white,  and  various 
combinations  of  colors.  For  example,  Fig.  65  may  be 
combined  by  means  of  double  images  (produced  by 
converging  or  diverging  the  optical  axes)  so  that  the 
two  inner  squares  are  coincident.  Actual  observation 
is  much  more  satisfactory  than  a  detailed  description. 

Miscellaneous.  —  There  are  many  interesting  ef- 
fects due  to  diffraction  of  light  by  edges  of  objects, 
by  meshes  such  as  a  wire  screen  or  a  handkerchief, 
by  the  eye-media,  etc.  On  looking  at  a  very  bright 
small  light-source  it  may  be  seen  to  be  surrounded 
by  many  colors. 

Streamers  of  light  appear  to  radiate  from  brilliant 


COLOR  143 


sources  and  all  bright  areas  colored  or  colorless,  when 
viewed  amid  dark  surroundings,  appear  to  be  sur- 
rounded by  diffuse  brushes  of  light.  These  brushes 
are  likely  to  be  of  a  bluish  tint. 

Many  of  these  phenomena  are  readily  explained, 
but  this  cannot  be  done  safely  without  knowing  or 
recognizing  all  conditions.  Many  are  not  easily  ex- 
plained, especially  when  reported  by  others,  who  may 
not  recognize  certain  important  conditions.  For  ex- 
ample, authentic  observers  have  reported  that  black 
letters  on  white  paper  appeared  vivid  red  on  a  white 
background,  under  certain  conditions.  Of  the  latter, 
the  apparently  important  one  was  "  sun's  rays  falling 
aslant  the  forehead."  When  the  eyes  were  shaded 
with  the  hand  the  letters  immediately  appeared  black 
as  they  should. 

The  influence  of  the  color  of  an  object  upon  its 
apparent  weight  is  relatively  slight,  but  there  is  evi- 
dence of  a  tendency  to  judge  a  red  or  black  object  to 
be  slightly  heavier  than  a  yellow  or  blue  object  of  the 
same  weight.  It  appears  that  hue  is  a  minor  factor 
in  influencing  the  judgment  and  that  there  is  no  cor- 
relation between  the  affective  quality  of  a  color  and 
its  influence  upon  apparent  weight.  Although  the 
scanty  evidence  available  attributes  but  a  slight 
influence  to  color  in  this  respect,  it  is  of  interest  in 
passing  as  a  reminder  of  the  many  subtle  factors 
which  are  at  work  modifying  our  judgments. 


X 

LIGHTING 

IT  should  be  obvious  by  this  time  that  the  lighting 
of  objects  or  of  a  scene  can  alone  produce  an 
illusion,  and  that  it  can  in  still  more  cases  con- 
tribute toward  an  illusion.  Furthermore,  there  are 
many  cases  of  illusions  in  lighting  due  to  brightness 
and  color.  Many  effects  of  lighting  have  been  de- 
scribed elsewhere  with  detailed  analyses  of  the  under- 
lying principles,  but  a  condensed  survey  applying 
particularly  to  illusions  will  be  presented  here. 

The  comparison  of  intaglio  with  low  relief  has 
been  mentioned  several  times  in  preceding  chapters. 
Examples  of  these  as  related  to  lighting  are  found  in 
Figs.  70  to  73.  Fig.  70  represents  a  bas-relief  lighted 
from  above  and  Fig.  71  would  ordinarily  be  taken  to 
represent  a  bas-relief  lighted  from  below.  However, 
the  latter  was  made  from  a  photograph  of  the  mold 
(intaglio)  from  which  the  bas-relief  was  made  and 
Fig.  71  really  represents  an  intaglio  lighted  from 
above. 

Similarly  Fig.  72  represents  the  bas-relief  lighted 
from  the  left  and  Fig.  73  ordinarily  would  be  taken 
to  be  a  bas-relief  lighted  from  the  right.  However, 
Fig.  73  was  made  from  a  photograph  of  an  intaglio 
lighted  from  the  left.  These  amply  demonstrate  the 
effect  of  lighting  as  an  influence  upon  the  appearance 

144 


LIGHTING  146 


of  objects  and  they  indicate  the  importance  of  correct 
assumptions  in  arriving  at  a  correct  judgment.  In 
these  cases  the  concealment  of  the  light-source  and 
the  commonness  of  bas-relief  as  compared  with 


a  b 

Fig.  74.  —  a.  A  disk  (above)  and  a  sphere  (below)  lighted  from  overhead. 
&.  A  disk  and  a  sphere  lighted  by  perfectly  diffused  light. 

intaglio  are  the  causes  for  the  illusion  or  the  error  in 
judgment.  Certainly  in  these  cases  the  visual  sense 
delivers  its  data  correctly. 

In  Fig.  74  the  upper  object  is  a  disk  and  the 
lower  is  a  sphere.    In  a  Fig.  74  the  lighting  is  due 


146 


VISUAL  ILLUSIONS 


Fig.  70.  —  A  bas-relief  lighted  from  above. 


LIGHTING  147 


'mm 


Fig.  71.  —  An  intaglio  lighted  from  above. 


148 


VISUAL  ILLUSIONS 


Fig.  72. —  A  bas-relief  lighted  from  the  left. 


LIGHTING 


149 


Fig.  73.  —  An  intaglio  lighted  from  the  left. 


150  VISUAL  ILLUSIONS 

to  a  source  of  light  of  rather  small  physical  dimensions 
directly  above  the  objects.  The  same  objects  il- 
luminated by  means  of  highly  diffused  light  (that  is, 
light  from  many  directions  and  of  uniform  intensity) 
appear  as  in  b.  Both  objects  now  appear  as  disks. 
It  is  obvious  that  under  appropriate  lighting  a  disk 
might  be  taken  for  a  sphere  and  vice  versa,  depend- 


Fig.  76.  —  A  concave  hemispherical  cup  on  the  left  and  a  convex  hemisphere 
on  the  right  lighted  by  a  light-source  of  large  angle  such  as  a  window. 

ing  upon  which  dominates  the  judgment  or  upon  the 
formulation  of  the  attendant  assumptions.  Incident- 
ally an  appearance  quite  similar  to  that  of  a,  Fig.  74 
is  obtained  when  the  light-source  is  near  the  ob- 
server; that  is,  when  it  lies  near  the  line  of  sight. 

Somewhat  similar  to  the  confusion  of  intaglio 
with  bas-relief  is  the  confusion  of  the  two  hemi- 
spherical objects  illustrated  in  Fig.  75.  The  one  on 
the  left  is  concave  toward  the  observer.  In  other 
words,  both  could  be  hemispherical  shells  —  one  a 
mold  for  the  other.  Under  the  lighting  which  existed 
when  the  original  photographs  were  made  they  could 
both  be  taken  for  hemispheres.  The  lighting  was  due 
to  a  large  light-source  at  the  left,  but  if  the  object 


LIGHTING  151 


on  the  left  is  assumed  (incorrectly)  to  be  a  hemisphere 
convex  toward  the  observer  or  a  sphere,  it  must  be 
considered  to  be  lighted  from  the  right,  which  is  also 
an  incorrect  assumption.  Obviously,  if  the  direction 
of  the  dominant  light  is  clear  to  the  observer,  he  is 
not  likely  to  make  the  error  in  judgment.  Incidentally 
the  object  on  the  right  might  be  assumed  to  be  a 


Fig.  76.  —  The  same  as  Fig.  75,  but  lighted  by  a  very  small  light-source. 

sphere    because    a    sphere    is   more    commonly    en- 
countered than  a  hemisphere. 

The  same  objects  are  represented  in  Fig.  76 
lighted  from  the  left  by  means  of  a  light-source  of 
relatively  small  dimensions;  that  is,  a  source  sub- 
tending a  relatively  small  solid-angle  at  the  objects. 
In  this  case  the  sharp  shadow  due  to  the  edge  of  the 
hemispherical  cup  (on  the  left)  is  likely  to  cause  the 
observer  to  inquire  further  before  submitting  his 
judgment.  The  more  gradual  modulation  of  light 
and  shade  as  in  the  case  of  a  sphere  or  a  hemisphere 
convex  toward  the  observer  is  not  present  in  the  case 
of  the  cup.  This  should  be  sufficient  information  for 
the  careful  observer  to  guide  him,  or  at  least  to  prevent 


152  VISUAL  ILLUSIONS 

him  from  arriving  at  the  definite  conclusion  that  the 
left-hand  object  is  a  hemisphere  with  its  convex  side 
toward  him.  Furthermore  it  should  be  noted  that  we 
often  jump  at  the  conclusion  that  an  object  is  a  sphere 
even  though  we  see  with  one  eye  practically  only  a 
hemisphere  and  with  two  eyes  hardly  enough  more 
to  justify  such  a  conclusion.  However,  spheres  are 
more  commonly  encountered  than  hemispheres,  so  we 
take  a  chance  without  really  admitting  or  even  recog- 
nizing that  we  do. 

The  foregoing  figures  illustrate  several  phases 
which  influence  our  judgments  and  the  wonder  is 
that  we  do  not  make  more  errors  than  we  do.  Of 
course,  experience  plays  a  large  part  and  fortunately 
experience  can  be  depended  upon  in  most  cases; 
however,  in  the  other  cases  it  leads  us  astray  to  a 
greater  extent  than  if  we  had  less  of  it. 

The  photographer,  perhaps,  recognizes  more  than 
anyone  else  the  pitfalls  of  lighting  but  it  is  unfortu- 
nate that  he  is  not  better  acquainted  with  the  funda- 
mentals underlying  the  control  of  light.  Improper 
lighting  does  produce  apparent  incongruous  effects 
but  adequately  controlled  it  is  a  powerful  medium 
whose  potentiality  has  not  been  fully  realized.  The 
photographer  aims  to  illuminate  and  to  pose  the 
subject  with  respect  to  the  source  or  sources  of  light 
so  that  undesirable  features  are  suppressed  and 
desirable  results  are  obtained. 

Finally  his  work  must  be  accepted  by  others  and 
the  latter,  being  human,  possess  (unadmittedly  of 
course)  a  desire  to  be  "  good  looking."  Lighting 
may  be  a  powerful  flatterer  when  well  controlled 


LIGHTING  153 


and  may  be  a  base  revealer  or  even  a  creator  of  ugli- 
ness. 

Incidentally,  the  photographer  is  always  under 
the  handicap  of  supplying  a  "  likeness  "  to  an  indi- 
vidual who  perhaps  never  sees  this  same  "  likeness  " 
in  a  mirror.  In  other  words,  the  image  which  a  person 
sees  of  himself  in  a  mirror  is  not  the  same  in  general 
that  the  photographer  supplies  him  in  the  photo- 
graphic portrait.  The  portrait  can  be  a  true  likeness 
but  the  mirrored  image  in  general  cannot  be.  In 
the  mirror  there  is  a  reversal  of  the  parts  from  right 
to  left.  For  example,  a  scar  on  the  right  cheek  of  the 
actual  face  appears  on  the  left  cheek  in  the  mirror. 
Faces  are  not  usually  symmetrical  and  this  reversal 
causes  an  individual  to  be  familiar  with  his  own 
facial  characteristics  in  this  reversed  form.  This 
influence  is  very  marked  in  some  cases.  For  example, 
suppose  the  left  side  of  a  companion's  face  to  be 
somewhat  paralyzed  on  one  side  due  to  illness.  We 
have  become  more  or  less  oblivious  to  the  altered 
expression  of  the  left  side  by  seeing  it  so  often.  How- 
ever, if  we  catch  a  glimpse  of  this  companion's  face 
in  the  mirror  and  the  altered  expression  of  the  left 
side  now  appears  upon  the  right  side  of  the  face,  the 
contrast  makes  the  fact  very  conspicuous.  Perhaps 
this  accounts  for  the  difference  which  exists  between 
the  opinions  of  the  photographer  (or  friends)  and 
of  the  subject  of  the  portrait. 

All  the  illusions  of  brightness-contrast  may  be 
produced  by  lighting.  Surfaces  and  details  may 
appear  larger  or  smaller,  harsh  or  almost  obliterated, 
heavy  or  light;  in  fact,  lighting  plays  an  important 


154  VISUAL  ILLUSIONS 

part  in  influencing  the  mood  or  expression  of  a  room. 
A  ceiling  may  be  "  lifted  "  by  light  or  it  may  hang 
low  and  threatening  when  dark,  due  to  relatively 
little  light  reaching  it.  Columns  may  appear  dark 
on  a  light  background  or  vice  versa,  and  these  illus- 
trate the  effects  of  irradiation.  A  given  room  may  be 
given  a  variety  of  moods  or  expressions  by  varying 
the  lighting  and  inasmuch  as  the  room  and  its  physical 
characteristics  have  not  been  altered,  the  various 
moods  may  be  considered  to  be  illusions.  It  should 
be  obvious  that  lighting  is  a  potent  factor. 

In  connection  with  lighting  it  should  be  noted 
that  contrasts  play  a  prominent  role  as  they  always 
do.  These  have  been  discussed  in  other  chapters, 
but  it  appears  advantageous  to  recall  some  of  the 
chief  features.  The  effect  of  contrast  is  always  in 
the  direction  of  still  greater  contrast.  That  is,  black 
tends  to  make  its  surroundings  white;  red  tends  to 
make  its  surroundings  blue-green  (complementary), 
etc.  The  contrast-effect  is  greatest  when  the  two 
surfaces  are  juxtaposed  and  the  elimination  of  bound- 
ary lines  of  other  colors  (including  black  or  white) 
increases  its  magnitude.  The  contrast-effect  of  colors 
is  most  conspicuous  when  there  is  no  brightness- 
contrast,  that  is,  when  the  two  surfaces  are  of  equal 
brightness  and  therefore  differ  chiefly  in  hue.  This 
effect  is  also  greatest  for  saturated  colors.  It  has 
been  stated  that  cold  colors  produce  stronger  con- 
trast-effects than  warm  colors,  but  experimental  evi- 
dence is  not  sufficiently  plentiful  and  dependable  to 
verify  this  statement. 

As  the  intensity  of  illumination  increases,  colors 


LIGHTING  155 


appear  to  become  less  saturated.  For  example,  a 
pure  red  object  under  the  noonday  sun  is  likely  to  be 
painted  an  orange  red  by  the  artist  because  it  does 
not  appear  as  saturated  as  it  would  under  a  much 
lower  intensity  of  illumination.  In  general,  black  and 
white  are  the  final  appearances  of  colors  for  respec- 
tively very  low  and  very  high  brightness.  As  the 
intensity  of  illumination  decreases,  hue  finally  dis- 
appears and  with  continued  decrease  the  color  ap- 
proaches black.  Conversely,  as  the  intensity  of  il- 
lumination increases,  a  color  becomes  apparently  less 
and  less  saturated  and  tends  toward  white.  For 
example,  on  viewing  the  sun  through  a  colored  glass 
the  sun  appears  of  a  much  less  saturated  color  than 
the  haze  near  the  sun  or  a  white  object  illuminated 
by  sunlight. 

Visual  adaptation  also  plays  a  prominent  part,  and 
it  may  be  stated  that  all  sensations  of  light  tend  toward 
a  middle  gray  and  all  sensations  of  color  tend  toward 
neutrality  or  a  complete  disappearance  of  hue.  The 
tendency  of  sensations  of  light  toward  a  middle  gray 
is  not  as  easily  recognized  as  changes  in  color  but 
various  facts  support  this  conclusion.  In  lighting  it 
is  important  to  recognize  the  tendency  of  color  toward 
neutrality.  For  example,  a  warm  yellow  light  soon 
disappears  as  a  hue  and  only  its  subtle  influence  is 
left;  however,  a  yellow  vase  still  appears  yellow 
because  it  is  contrasted  with  objects  of  other  colors. 
In  the  case  of  colored  light  the  light  falls  upon  every- 
thing visible,  and  if  there  is  no  other  light-source  of 
another  color  with  which  to  contrast  it,  its  color  ap- 
pears gradually  to  fade.  This  is  an  excellent  example 


156  VISUAL  ILLUSIONS 

of  the  tremendous  power  and  importance  of  contrast. 
It  is  the  life  of  color  and  it  must  be  fully  appreciated 
if  the  potentiality  of  lighting  is  to  be  drawn  upon  as 
it  should  be. 

Physical  measurements  are  as  essential  in  lighting 
as  in  other  phases  of  human  endeavor  for  forming 
a  solid  foundation,  but  in  all  these  activities  where 
visual  perception  plays  an  important  part  judgment 
is  finally  the  means  for  appraisal.  Wherever  the 
psychological  aspect  is  prominent  physical  measure- 
ments are  likely  to  be  misleading  if  they  do  not  agree 
with  mental  appraisals.  Of  course  the  physical  meas- 
urements should  be  made  and  accumulated  but  they 
should  be  considered  not  alone  but  in  connection 
with  psychological  effects. 

The  photometer  may  show  a  very  adequate  in- 
tensity of  illumination;  nevertheless  seeing  may  be 
unsatisfactory  or  even  impossible.  An  illumination 
of  a  few  foot-candles  under  proper  conditions  at  a 
given  surface  is  quite  adequate  for  reading;  how- 
ever, this  surface  may  appear  quite  dark  if  the  sur- 
roundings are  bright  enough.  In  such  a  case  the 
photometer  yielded  results  quite  likely  to  be  misin- 
terpreted as  satisfactory.  It  should  be  obvious  that 
many  illusions  discussed  in  preceding  chapters  are 
of  interest  in  this  connection. 

An  interesting  example  of  the  illusion  of  color 
may  be  easily  demonstrated  by  means  of  a  yellow 
filter.  For  this  purpose  a  canary  glass  is  quite  satis- 
factory. When  such  a  filter  is  placed  before  the  eyes 
a  daytime  scene  outdoors,  for  example,  is  likely  to 
appear  to  be  illuminated  to  a  greater  intensity  than 


LIGHTING  167 


when  the  eyes  are  not  looking  through  the  filter.  This 
is  true  for  a  glass  used  by  the  author  notwithstanding 
the  fact  that  the  filter  transmits  only  about  one-half 
as  much  light  as  a  perfectly  clear  colorless  glass.  In 
other  words,  the  brightnesses  of  objects  in  the  scene 
are  reduced  on  the  average  about  fifty  per  cent,  still 
the  subject  is  impressed  with  an  apparent  increase 
in  the  intensity  of  illumination  (and  in  brightness) 
when  the  filter  is  placed  before  the  eyes.  Of  course, 
the  actual  reduction  in  brightness  depends  upon  the 
color  of  the  object. 

In  such  a  case  as  the  foregoing,  true  explanations 
are  likely  to  involve  many  factors.  For  this  reason 
explanations  are  usually  tedious  if  they  are  to  be 
sufficiently  qualified  to  be  reasonably  near  complete- 
ness. In  this  case  it  appears  that  the  yellow  filter 
may  cause  one  to  appraise  the  intensity  of  illumina- 
tion as  having  increased,  by  associating  such  an  in- 
fluence as  the  sun  coming  out  from  behind  a  cloud. 
If  we  look  into  the  depths  where  light  and  color  ac- 
cumulated their  psychological  powers,  we  are  con- 
fronted on  every  hand  by  associations  many  of  which 
are  more  or  less  obscure,  and  therefore  are  subtly 
influential. 

The  psychological  powers  of  colors  could  have 
been  discussed  more  generally  in  the  preceding  chap- 
ter, but  inasmuch  as  they  can  be  demonstrated  more 
effectively  by  lighting  (and  after  all  the  effect  is  one 
of  light  in  any  case)  they  will  be  discussed  briefly 
here.  They  have  been  presented  more  at  length 
elsewhere. 

It  is  well  known  that  the  artist,  decorator,  and 


158  VISUAL  ILLUSIONS 

others  speak  of  warm  and  cold  colors,  and  these  ef- 
fects have  a  firm  psychological  foundation.  For  ex- 
ample, if  a  certain  room  be  illuminated  by  means  of 
blue  light,  it  does  seem  colder.  A  theater  illuminated 
by  means  of  bluish  light  seems  considerably  cooler 
to  the  audience  than  is  indicated  by  the  thermometer. 
If  this  lighting  is  resorted  to  in  the  summer  time  the 
theater  will  be  more  inviting  and,  after  all,  in  such 
a  case  it  makes  little  difference  what  the  thermometer 
indicates.  The  "  cold "  light  has  produced  an  il- 
lusion of  coolness.  Similarly  "  warm  "  light,  such  as 
yellow  or  orange,  is  responsible  for  the  opposite 
feeling  and  it  is  easily  demonstrated  that  an  illusion 
of  higher  temperature  may  be  produced  by  its  use. 
As  already  stated,  color-schemes  in  the  decorations 
and  furnishings  produce  similar  effects  but  in  general 
they  are  more  powerful  when  the  primary  light  is 
colored.  In  the  latter  case  no  object  is  overlooked 
for  even  the  hands  and  faces  of  the  beings  in  the 
room  are  colored  by  the  light.  In  the  case  of  color- 
schemes  not  all  objects  are  tinged  with  the  desired 
"  warm  "  or  "  cold  "  color. 

In  the  foregoing,  associations  play  a  prominent 
role.  The  sky  has  been  blue  throughout  the  number- 
less centuries  during  which  the  human  organism 
evolved.  The  blue-sky  during  all  these  centuries 
has  tinged  the  shadows  outdoors  a  bluish  color.  That 
shade  is  relatively  cool  we  know  by  experience  and 
perhaps  we  associate  coolness  or  cold  with  the  aerial 
realm.  These  are  glimpses  of  influences  which  have 
cooperated  toward  creating  the  psychological  effect 
of  coldness  in  the  case  of  bluish  light.  By  contrast 


LIGHTING  169 


with  skylight,  sunlight  is  yellowish,  and  a  place  in 
the  sun  is  relatively  warm.  South  rooms  are  usually 
warmer  than  north  rooms  in  this  hemisphere  when 
artificial  heat  is  absent  and  the  psychological  effect 
of  warmth  has  naturally  grown  out  of  these  and  similar 
influences. 

We  could  go  further  into  the  psychology  of  light 
and  color  and  conjecture  regarding  effects  directly 
attributable  to  color,  such  as  excitement,  depression, 
and  tranquillity.  In  so  doing  we  would  be  led  far 
astray  from  illusions  in  the  sense  of  the  term  as  used 
here.  Although  this  term  as  used  here  is  still  some- 
what restricted,  it  is  broader  in  scope  than  in  its 
usual  applications.  However,  it  is  not  broad  enough 
to  lead  far  into  the  many  devious  highways  and  by- 
ways of  light  and  color.  If  we  did  make  these  ex- 
cursions we  would  find  associations  almost  univer- 
sally answering  the  questions.  The  question  would 
arise  as  to  innate  powers  of  colors  and  we  would  find 
ourselves  wondering  if  all  these  powers  were  ac- 
quired (through  associations)  and  whether  or  not 
some  were  innate.  And  after  many  interesting  views 
of  the  intricate  subject  we  would  likely  conclude  that 
the  question  of  the  innateness  of  some  of  the  powers 
of  color  must  be  left  unanswered. 

As  an  example  let  us  take  the  case  of  the  rest- 
fulness  or  depression  due  to  blue.  We  note  that  the 
blue  sky  is  quite  serene  or  tranquil  and  we  find  that 
the  delicate  sensibilities  of  poets  verify  this  im- 
pression. This  association  could  account  for  the  im- 
pression or  feeling  of  tranquillity  associated  with  blue. 
On  proceeding  further,  we  would  find  nature's  soli- 


160  VISUAL  ILLUSIONS 

tudes  often  tinged  with  the  blue  skylight,  for  these 
solitudes  are  usually  in  the  shade.  Thus  their  rest- 
fulness  or  even  depressiveness  may  be  accounted 
for  —  partially  at  least.  These  brief  glimpses  are 
presented  in  order  that  they  may  suggest  to  the  reader 
another  trend  of  thought  when  certain  illusions  of 
light  and  color  are  held  up  for  analysis.  Besides 
these  our  individual  experiences  which  have  molded 
our  likes  and  dislikes  must  be  taken  into  account. 
This  phase  of  light  and  color  has  been  treated  else- 
where.6 

A  very  unusual  kind  of  optical  illusion  is  illustrated 
by  the  phenomenon  of  the  apparent  ending  of  a  search- 
light beam  which  has  attracted  much  attention  in 
connection  with  the  powerful  searchlights  used  for 
locating  aeroplanes  (Fig.77).  For  years  the  apparent 
ending  has  more  or  less  carelessly  been  attributed 
to  the  diminution  of  the  density  of  atmospheric  fog 
or  haze,  but  recently  Karrer 13  has  suggested  what 
appears  to  be  the  correct  explanation. 

When  the  beam  of  light  from  a  powerful  searchlight 
is  directed  into  space,  its  path  is  visible  owing  to  the 
scattering  of  some  of  the  light  by  dust  and  moisture 
particles  and  the  molecules  of  the  air  itself.  While 
obviously  the  beam  itself  must  go  on  indefinitely,  its 
luminous  path  appears  to  end  abruptly  at  no  very 
great  distance  from  the  source.  This  is  true  whether 
the  beam  is  photographed  or  viewed  with  the  naked 
eye. 

The  fact  that  the  appearance  of  the  beam  is  no  dif- 
ferent when  it  is  directed  horizontally  than  when 
directed  vertically  proved  that  the  common  assump- 


LIGHTING  161 


tion  pertaining  to  the  ending  of  the  haze  or  fog  is 
untenable.  Furthermore,  photometric  measurements 
on  the  different  portions  of  the  beam  as  seen  from  a 


Fig.  77.  —  Apparent  ending  of  a  searchlight  beam. 

position  near  the  searchlight  show  that  the  beam  is 
actually  brighter  at  its  outer  termination  than  near 
its  origin.  Again,  the  apparent  length  of  the  beam 


162  VISUAL  ILLUSIONS 

varies  with  the  position  of  the  observer,  and  bears  a 
direct  ratio  to  his  distance  from  the  searchlight. 

The  fact  is,  that  the  luminous  path  of  the  beam  has 
no  definite  ending,  and  extends  to  a  very  great  dis- 
tance—  practically,  to  infinity.  It  appears  to  be 
sharply  cut  off  for  the  same  reason  that  the  boundary 
between  earth  and  sky  in  a  flat  landscape  is  a  sharp 
line.  Just  as  the  horizon  recedes  when  the  landscape 
is  viewed  from  an  elevation,  so  the  beam  appears 
longer  when  one's  distance  from  it  is  increased.  The 
outer  portion  appears  brighter,  because  here  the  line 
of  sight  pierces  it  to  great  depth. 

That  the  ending  of  the  beam  appears  close  at  hand 
is  no  doubt  partly  due  to  the  brightness  distribution, 
but  is  also  a  matter  of  perspective  arising  from  the 
manner  in  which  the  beam  is  adjusted.  Searchlight 
operators  in  the  army  were  instructed  to  adjust  the 
light  to  throw  a  parallel  beam.  Accordingly,  the  ad- 
justments were  so  made  that  the  beam  appeared  the 
same  width  at  its  outer  extremity  as  at  its  base.  The 
result  seems  to  be  a  short  parallel  shaft  of  light,  but 
is  really  a  divergent  cone  of  infinite  extent,  its  angle 
of  divergence  being  such  as  exactly  to  offset  the  effects 
of  perspective. 

If  the  beam  were  a  truly  parallel  one  it  would  seem 
to  come  to  a  point,  just  as  the  edges  of  a  long  straight 
stretch  of  country  road  seem  to  meet  at  the  horizon. 
If  the  sides  of  the  road  were  not  parallel,  but  diverged 
from  the  observer's  eye  at  exactly  the  rate  at  which 
they  ordinarily  would  appear  to  converge,  then  the 
road  would  seem  to  be  as  wide  where  it  passed  out 
at  the  horizon  as  at  the  observer's  feet.  If  there  were 


LIGHTING  163 


no  other  means  in  the  landscape  of  judging  the  dis- 
tance of  the  horizon  than  by  the  perspective  afforded 
by  the  road,  it  would  likely  be  inferred  that  the  road 
only  extended  a  short  distance  on  the  level,  and  then 
went  down  a  hill,  that  is,  passed  abruptly  from  the 
observer's  view. 

These  conditions  obtain  ideally  in  the  case  of  the 
searchlight  beam.  There  is  no  other  means  of  judging 
the  position  in  space  of  the  "  end  "  of  an  unobstructed 
searchlight  beam  than  by  the  perspective  of  the  beam 
itself,  and  the  operator  in  adjusting  it  to  appear  parallel 
eliminates  the  perspective. 

The  angle  at  which  the  beam  must  diverge  to  appear 
parallel  to  an  observer  depends  upon  the  distance  of 
the  observer  from  the  searchlight.  A  beam  which 
seems  parallel  to  a  person  close  to  it  will  not  appear 
so  at  a  distance.  This  fact  probably  accounts  for  the 
difficulties  encountered  during  "  searchlight  drill"  in 
the  army  in  getting  a  beam  which  satisfied  both  the 
private  operating  the  lamp  and  the  officer  down  the 
field  as  to  its  parallelity. 

To  summarize,  the  apparent  abrupt  ending  of  a 
searchlight  beam  is  purely  an  optical  illusion.  It 
really  has  no  ending;  it  extends  to  infinity. 


XI 
NATURE 

VSUAL  illusions  abound  everywhere,  and  there 
are  a  number  of  special  interest  in  nature. 
Inasmuch  as  these  are  representative  of  a 
wide  range  of  conditions  and  are  usually  within  the 
possible  experience  of  nearly  everyone  daily,  they 
appear  worthy  of  special  consideration.  Some  of 
these  have  been  casually  mentioned  in  other  chap- 
ters but  further  data  may  be  of  interest.  No  agree- 
ment has  been  reached  in  some  cases  in  the  many 
suggested  explanations  and  little  or  no  attempt  of  this 
character  will  be  made  in  the  following  paragraphs. 
Many  illusions  which  may  be  seen  in  nature  will  be 
passed  by  because  their  existence  should  be  obvious 
after  reading  the  preceding  chapters.  For  example, 
a  tree  appears  longer  when  standing  than  after  it  has 
been  felled  for  the  same  reason  that  we  overestimate 
vertical  lines  in  comparison  with  horizontal  ones. 
The  apparent  movement  of  the  sun,  moon,  and  stars, 
when  clouds  are  floating  past,  is  a  powerful,  though 
commonplace,  illusion  but  we  are  more  specifically 
interested  in  static  illusions.  However,  it  is  of  in- 
terest to  recall  the  effect  of  involuntary  eye-move- 
ments or  of  fluctuation  in  fixation  because  this  factor 
in  vision  is  important  in  many  illusions.  It  is  demon- 
strated by  lying  face  upward  on  a  starlit  night  and 

164 


NATURE  165 


fixing  the  gaze  upon  a  star.  The  latter  appears  to  move 
more  or  less  jerkily  over  its  dark  background.  The 
magnitude  and  involuntary  nature  of  these  eye-move- 
ments is  demonstrated  in  this  manner  very  effectively. 

The  effect  sometimes  known  as  aerial  perspective 
has  been  mentioned  heretofore.  The  atmosphere 
is  not  perfectly  transparent  or  colorless  and  is  not 
homogeneous  from  an  optical  standpoint.  It  scatters 
rays  of  the  shorter  wave-lengths  more  than  those 
of  the  longer  wave-lengths.  Hence  it  appears  of  a 
bluish  tint  and  anything  seen  through  great  distances 
of  it  tends  toward  a  reddish  color.  The  blue  sky  and 
the  redness  of  the  setting  sun  are  results  of  this 
cause.  Distant  signal-lights  are  reddened,  due  to  the 
decrease  in  the  rays  of  shorter  wave-length  by 
scattering.  Apparently  we  have  come  to  estimate 
distance  to  some  extent  through  the  amount  of  blurring 
and  tinting  superposed  upon  the  distant  scene. 

In  the  high  Rockies  where  the  atmosphere  is 
unusually  clear,  stretches  of  fifty  miles  of  atmosphere 
lying  between  the  observer  and  the  distant  peaks  will 
show  very  little  haze.  A  person  inexperienced  in 
the  region  is  likely  to  construe  this  absence  of  haze 
as  a  shorter  distance  than  the  reality  and  many  amus- 
ing incidents  and  ludicrous  mistakes  are  charged 
against  the  tenderfoot  in  the  Rockies.  After  mis- 
judging distance  so  often  to  his  own  discomfiture  a 
tourist  is  said  to  have  been  found  disrobing  pre- 
paratory to  swimming  across  an  irrigation  ditch.  He 
had  lost  confidence  in  his  judgment  of  distance  and 
was  going  to  assume  the  risk  of  jumping  across  what 
appeared  to  be  a  ditch  but  what  might  be  a  broad 


166  VISUAL  ILLUSIONS 

river.  Of  course,  this  story  might  not  be  true  but  it 
serves  as  well  as  any  to  emphasize  the  illusion  which 
arises  when  the  familiar  haze  is  not  present  in  strange 
territory. 

It  is  a  common  experience  that  things  "  loom  in 
a  fog,"  that  is,  that  they  appear  larger  than  they 
really  are.  An  explanation  which  has  been  offered 
is  that  of  an  "  excess  of  aerial  perspective  "  which 
causes  us  to  overestimate  distance  and  therefore  to 
overestimate  size.  If  this  explanation  is  correct,  it  is 
quite  in  the  same  manner  that  in  clear  atmosphere 
in  the  mountains  we  underestimate  distance  and, 
consequently,  size.  However,  another  factor  may 
enter  in  the  latter  case,  for  the  illusion  is  confined 
chiefly  to  newcomers;  that  is,  in  time  one  learns 
to  judge  correctly.  On  entering  a  region  of  real  moun- 
tains the  first  time,  the  newcomer's  previous  ex- 
perience with  these  formations  is  confined  to  hills 
relatively  much  smaller.  Even  allowing  consider- 
ably for  a  greater  size  when  viewing  the  majestic 
peaks  for  the  first  time,  he  cannot  be  expected  to  think 
in  terms  of  peaks  many  times  larger  than  his  familiar 
hills.  Thus  underestimating  the  size  of  the  great 
peaks,  he  underestimates  the  distance.  The  rarity 
of  the  atmospheric  haze  aids  him  in  making  this  mis- 
take. This  is  not  offered  as  a  substitute  for  aerial 
perspective  as  the  primary  cause  of  the  illusion  but  it 
appears  to  the  author  that  it  is  a  cause  which  must 
be  taken  into  account. 

The  apparent  form  of  the  sky  has  attracted  the 
attention  of  many  scientific  investigators  for  centuries. 
There  are  many  conflicting  opinions  as  to  the  causes 


NATURE  167 


of  this  appearance  of  form,  but  there  is  general  agree- 
ment that  the  sky  appears  usually  as  a  flattened  vault. 
The  sky  is  bright,  due  to  scattering  of  light  by  actual 
particles  of  solid  matter  and  moisture  and  possibly 
by  molecules  of  gas.  Lack  of  optical  homogeneity 
due  to  varying  refractive  index  is  likely  to  be  partially 
responsible.  Usually  a  prominent  layer  of  haze  about 
a  mile  in  thickness  (although  this  varies  consider- 
ably) lies  next  to  the  earth's  surface.  The  top  of  this 
haze  is  fairly  well  defined  as  aerial  travelers  know, 
but  the  sky  above  is  still  far  from  black,  indicating 
scattered  light  and  illuminated  particles  still  higher. 
As  one  continues  to  ascend,  thereby  leaving  more  and 
more  of  the  luminous  haze  behind,  the  sky  becomes 
darker  and  darker.  Often  at  altitudes  of  four  or  five 
miles  the  sky  is  very  dark  and  the  sun  is  piercingly 
bright.  Usually  there  is  little  or  no  bright  haze  ad- 
jacent to  the  sun  at  these  high  altitudes  as  is  com- 
monly seen  from  the  earth's  surface.  At  these  high 
altitudes  the  author  is  not  conscious  of  a  flattened 
vault  as  at  the  earth's  surface  but  the  illusion  of  a 
hemispherical  dome  still  persists. 

There  is  some  agreement  that  the  dome  of  the 
sky  appears  less  depressed  at  the  zenith  by  night  than 
by  day.  This  is  in  accord  with  the  author's  observa- 
tion at  very  high  altitudes  on  occasions  when  the 
sky  was  much  darker  than  when  viewed  from  the 
earth's  surface.  Dember  and  Uibe  assumed  the 
apparent  shape  as  a  part  of  a  sphere  (justifying  this 
assumption  to  their  satisfaction)  and  obtained  esti- 
mates of  the  apparent  depression  at  the  zenith.  They 
estimated  the  middle  point  of  the  arc  from  the  zenith 


168  VISUAL  ILLUSIONS 

to  the  horizon  and  then  measured  the  angular  alti- 
tude of  that  point.  They  found  that  the  degree  of 
clearness  of  the  sky  has  considerable  influence  upon 
the  apparent  height  and  they  state  that  the  sky  ap- 
pears higher  in  the  sub-tropics  than  in  Germany. 
On  very  clear  moonless  nights  they  found  that  the 
shape  of  the  sky-dome  differs  little  from  that  of  a 
hemisphere.  They  concluded  that  the  phenomenon 
is  apparently  due  to  optical  conditions  of  the  atmos- 
phere which  have  not  been  determined. 

It  is  of  interest  to  note  the  appearance  of  the 
sky  when  cumulus  clouds  are  present.  The  bases 
of  these  vary  in  height,  but  are  found  at  altitudes 
from  three  to  five  thousand  feet.  They  appear  to  form 
a  flat  roof  of  clouds  bending  downward  at  the  horizon, 
thus  giving  the  appearance  of  a  vaulted  but  flattened 
dome.  This  apparent  shape  does  not  differ  much  in 
clear  weather,  perhaps  due  largely  to  the  accus- 
tomedness  of  the  eye  and  to  the  degradation  of  color 
from  blue  to  gray  toward  the  horizon.  Furthermore 
the  lower  sky  is  usually  much  brighter  than  the  zenith 
and  the  latter  being  darker  appears  to  hang  lower. 
It  is  of  interest  to  note  how  persistent  is  the  illusion 
of  a  flattened  dome,  for  when  one  rises  rapidly  in  the 
air  and,  within  a  few  minutes,  is  on  the  level  with  the 
clouds  or  the  dense  low-lying  haze,  he  is  mildly  sur- 
prised to  find  these  are  levels  and  not  vaulted  roofs. 
Despite  the  fact  that  by  many  previous  experiences 
he  has  learned  what  to  expect,  the  feeling  of  mild 
surprise  is  born  each  time  on  ascending  rapidly. 

The  appearance  of  the  flattened  vault  of  the  sky 
is  held  by  some  to  account  for  the  apparent  enlarge- 


NATURE  169 


ment  of  the  sun,  moon,  and  the  constellations  at  the 
horizon.  That  is,  they  appear  more  distant  at  the 
horizon  and  we  instinctively  appraise  them  as  being 
larger  than  when  they  are  at  higher  altitudes.  It  is 
certain  that  these  heavenly  bodies  do  appear  much 
larger  when  they  are  rising  or  setting  than  when  they 
are  nearer  the  zenith.  In  fact,  this  is  one  of  the  most 
remarkable  and  surprising  illusions  which  exist. 
Furthermore  this  apparent  enlargement  has  been 
noted  universally,  still  many  persons  have  attributed 
it  to  an  actual  optical  magnification.  Although  we 
are  more  familiar  with  this  enlargement  in  connec- 
tion with  the  sun  and  moon,  it  still  persists  with  the 
constellations.  For  example,  Orion  is  apparently 
very  large;  in  fact,  this  is  the  origin  of  the  name. 
That  this  enlargement  is  an  illusion  can  be  shown  in 
several  ways  but  that  it  is  solely  due  to  the  influence 
of  the  apparent  flattened  form  of  the  sky  may  be 
doubted.  Certainly  the  moon  appears  greatly  en- 
larged while  near  the  horizon,  even  when  there  is 
doubt  as  to  an  appreciable  appearance  of  flattening 
of  the  sky-dome. 

Many  peculiar  conditions  and  prejudices  must 
be  taken  into  account.  For  example,  if  various  per- 
sons are  asked  to  give  an  idea  of  how  large  is  the 
disk  of  the  sun  or  moon,  their  answers  would  vary 
usually  with  the  head  of  a  barrel  as  the  maximum. 
However,  the  size  of  a  tree  at  a  distant  sky-line  might 
unhesitatingly  be  given  as  thirty  feet.  At  the  horizon 
we  instinctively  compare  the  size  of  the  sun,  moon, 
and  constellations  with  hills,  trees,  houses,  and  other 
objects,  but  when  the  former  are  high  toward  the 


170  VISUAL  ILLUSIONS 

zenith  in  the  empty  sky  we  may  judge  them  in  their 
isolated  position  to  be  nearer,  hence  smaller. 

Normally  the  retinal  image  grows  larger  as  the 
object  approaches,  but  this  same  sensation  also  arises 
when  an  object  grows  in  size  without  altering  its 
distance.  If  the  moon  be  viewed  through  field-glasses 
the  image  is  larger  than  in  the  case  of  the  unaided 
eyes,  but  it  is  quite  common  for  observers  to  state 
that  it  appears  smaller.  The  enlargement  may  be 
interpreted  as  approach  and  inasmuch  as  we,  through 
habit,  allow  for  enlargement  as  an  object  approaches, 
we  also  must  reduce  it  in  our  imagination  to  its  natural 
size.  Perhaps  in  this  case  we  overdo  this  reduction. 

James  states  that  the  increased  apparent  size 
of  the  moon  near  the  horizon  "  is  a  result  of  associa- 
tion and  probability.  It  is  seen  through  vaporous 
air  and  looks  dimmer  and  duskier  than  when  it  rides 
on  high;  and  it  is  seen  over  fields,  trees,  hedges, 
streams,  and  the  like,  which  break  up  the  intervening 
space  and  makes  us  the  better  realize  the  latter's 
extent."  Both  these  causes  may  make  the  moon 
seem  more  distant  when  it  is  at  low  altitudes  and  as 
its  visual  angle  grows  less,  we  may  think  that  it  must 
be  a  larger  body  and  we  so  perceive  it.  Certainly 
it  looks  particularly  large  when  a  well-known  object 
is  silhouetted  against  its  disk. 

Before  proceeding  further  with  explanations,  it 
may  be  of  interest  to  turn  to  Fig.  78  which  is  an  ac- 
curate tracing  of  the  path  of  the  moon's  image  across 
a  photographic  plate.  The  camera  was  placed  in  a 
fixed  position  and  the  image  of  the  moon's  disk  on 
rising  was  accurately  focused  on  a  panchromatic  plate. 


NATURE  171 


A  dense  red  filter  was  maintained  over  the  lens  through- 
out in  order  to  eliminate  the  effect  of  selective  ab- 
sorption of  the  atmosphere.  **trr*the  slightest  en- 
largement was  detected  in  the  width  of  the  path  near 
the  horizon  as  compared  with  that  at  the  highest 


Fig.  78.  —  An  accurate  tracing  from  a  photograph  (continual  exposure)  of 

the  moon  rising. 

altitude.  This  copy  was  made  because  it  was  thought 
better  for  reproduction  than  the  photograph  which 
would  require  a  half-tone.  This  is  positive  evidence 
that  the  phenomenon  is  an  illusion. 

Similarly  Fig.  79  is  a  copy  of  a  negative  of  several 
exposures  of  the  sun.  Owing  to  the  greater  bright- 
ness, continuous  exposure  was  not  considered  feasible. 
A  panchromatic  plate  and  red  filter  was  used  as  in 
the  case  of  the  moon.  The  various  exposures  were 


172  VISUAL  ILLUSIONS 

made  without  otherwise  adjusting  the  camera.    Again 
no  enlargement  at  the  horizon  was  found. 

Although  the  foregoing  is  conclusive  evidence  of 
the  illusory  character  of  the  enlargement  there  are 
other  ways  of  making  measurements.  On  viewing 


Fig.  79.  —  Accurate  tracings  from  a  photograph  (short  exposures  at 
intervals)  of  the  sun  setting. 

the  sun  at  the  horizon  a  bright  after-image  is  ob- 
tained. This  may  now  be  projected  upon  the  sky 
as  a  background  at  any  desired  altitude.  It  will  ap- 
pear much  smaller  at  the  zenith  than  the  sun  appears 
at  the  horizon.  Certainly  this  is  a  simple  and  con- 
clusive demonstration  of  the  illusion.  In  this  case 
the  after-image  of  the  sun  or  the  sun  itself  will  usually 
appear  at  least  twice  as  large  as  the  after-image 
at  the  zenith. 


NATURE  173 


If  the  variation  in  the  position  of  the  eyes  is  held 
to  account  for  the  illusion,  this  explanation  may  be 
supported  by  using  a  horizontal  telescope  with  ad- 
justable cross-hairs,  and  a  mirror.  By  varying  the 
position  of  the  latter  the  disk  of  the  sun  may  be  meas- 
ured at  any  altitude  without  varying  the  position 
of  the  eye.  When  everything  is  eliminated  from  the 
field  but  the  moon's  disk,  it  is  found  to  be  constant 
in  size.  However,  this  is  not  conclusive  evidence 
that  the  variation  in  the  position  of  the  line  of  sight 
accounts  for  the  illusion. 

As  a  demonstration  of  the  absence  of  enlargement 
of  the  size  of  the  moon  near  the  horizon  some  have 
brought  forward  measurements  of  the  lunar  circles 
and  similar  phenomena.  These  are  said  to  be  un- 
affected by  the  altitude  of  the  moon  except  for  re- 
fraction. But  even  this  does  not  change  the  horizontal 
diameter  and  actually  diminishes  the  vertical  one. 
The  moon  is  further  away  when  near  the  horizon 
than  when  at  the  zenith,  the  maximum  increase  in 
distance  being  one-half  the  diameter  of  the  earth. 
This  would  make  the  moon  appear  about  one-sixtieth, 
or  one-half  minute  of  arc  smaller  at  the  horizon  than 
at  the  zenith.  This  is  not  only  in  the  wrong  direction 
to  aid  in  accounting  for  the  apparent  enlargement,  but 
it  is  so  slight  as  to  be  imperceptible  to  the  unaided  eye. 

Nearly  two  centuries  ago  Robert  Smith  and  his 
colleagues  concluded  that  the  sky  appears  about 
three  times  as  far  away  at  the  horizon  as  at  the  zenith. 
They  found  that  the  relative  apparent  diameters 
of  the  sun  and  of  the  moon  varied  with  altitude  as 
follows : 


174 


VISUAL  ILLUSIONS 


Altitude 

Relative  apparent  diameter 

0  deg.  (horizon) 

100 

15  " 

68 

30  " 

50 

45  " 

40 

60  " 

34 

75  " 

31 

90  "     (zenith) 

30 

Fig.  80.  —  Explanation  offered  by  Smith  of  the  apparent  enlargement  of 
heavenly  bodies  near  the  horizon. 

They  also  found  a  similar  relation  between  the  alti- 
tude and  the  apparent  size  of  constellations.  Fig.  80 
is  a  reproduction  of  a  diagram  which  Smith  sub- 
mitted as  illustrating  the  cause  of  the  illusion  of 
apparent  enlargement  of  heavenly  bodies  near  the 
horizon.  If  the  sky  seems  to  be  a  flattened  vault, 
the  reason  for  the  apparent  decrease  in  the  size  of 
the  sun,  the  moon,  or  the  constellations,  as  they  ap- 
proach the  zenith,  is  suggested  by  the  diagram. 

It  has  also  been  suggested  that  such  illusions  as 
those  shown  in  Figs.  10  and  19  are  associated  with 
that  of  apparent  enlargement  of  heavenly  bodies  near 


NATURE  175 


the  horizon.  It  will  be  left  to  the  reader  to  decide 
whether  or  not  there  is  any  similarity  or  relation. 

Zoth  appears  to  have  proved,  to  his  own  satis- 
faction at  least,  that  the  chief  factors  are  not  aerial 
perspective,  the  apparent  curvature  or  form  of  the  sky, 
and  the  comparison  of  the  sun  or  moon  with  objects 
of  known  size.  He  maintained  that  the  illusion  of 
apparent  decrease  in  size  as  these  bodies  increase 
in  altitude  is  due  to  the  necessary  elevation  of  the 
eye.  No  available  experimental  evidence  seems  to 
refute  his  statement.  In  fact,  Guttman's  experi- 
ments seem  to  confirm  it  to  some  extent.  The  latter 
found  that  there  was  an  apparent  diminution  in  the 
size  of  objects  of  several  per  cent,  in  objects  slightly 
more  than  a  foot  distant  from  the  eyes,  as  they  were 
raised  so  that  the  line  of  vision  changed  from  hori- 
zontal to  an  angle  of  forty  degrees.  The  magnitude 
of  this  diminution  is  not  sufficient  to  promote  the  ac- 
ceptance of  elevation  of  the  eyes  as  a  primary  cause 
of  the  illusion  in  respect  to  the  heavenly  bodies. 

Notwithstanding  arguments  to  the  contrary,  it 
is  difficult  to  eliminate  aerial  perspective  and  the 
apparent  form  of  the  sky  as  important  factors.  That 
no  explanation  of  this  illusion  has  been  generally 
accepted  indicates  the  complexity  of  the  causes. 
Certainly  the  reddish  coloration  of  the  sun  and  moon 
near  the  horizon  and  the  contrast  with  the  misty 
atmosphere  combined  with  the  general  vague  aspect 
of  the  atmosphere  contribute  something  if  no  more 
than  a  deepening  of  the  mystery.  Variations  in  the 
transparency  and  brightness  of  the  air  must  play 
some  part. 


176  VISUAL  ILLUSIONS 

In  discussing  the  great  illusions  of  nature,  it  ap- 
pears appropriate  to  introduce  the  mirage.  This 
is  not  due  to  an  error  of  sense  of  judgment.  The 
eye  sees  what  is  presented  but  the  inversions  and 
other  peculiar  effects  are  due  to  variations  in  the 
refractive  index  of  the  atmosphere.  These  varia- 
tions account  for  the  appearance  of  "  lakes  "  in  arid 
deserts,  of  the  inverted  images  of  ships  and  ice- 
bergs on  the  sea  and  of  "  pools  of  water  "  on  pave- 


Fig.  81.  —  Explanation  of  a  common  mirage. 

ments.  The  refractive  index  of  the  atmosphere  is 
continually  changing,  but  the  changes  are  chiefly  of 
two  types:  (1)  those  due  to  irregular  heating  and 
(2)  those  due  to  normal  variation  with  altitude.  The 
former  type  are  particularly  responsible  for  mirages. 
A  common  type  of  mirage  is  illustrated  in  Fig.  81. 
This  is  often  visible  on  deserts  where  the  hot  sand 
causes  the  adjacent  layer  of  air  to  expand  and  there- 
fore, the  refractive  index  to  increase.  This  layer  of 
air  then  may  be  considered  to  operate  like  an  inverted 
prism.  The  rays  of  light  close  to  the  earth  are  bent 
convex  to  the  earth  and  the  curvature  of  those  higher 
up  may  be  reversed.  The  reason  that  an  object  may 


NATURE  177 


appear  double,  or  as  if  mirrored  by  the  surface  of  a 
nearby  pond,  is  clearly  shown  in  the  illustration. 

Similar  atmospheric  conditions  are  found  some- 
times over  pavements  and  over  bodies  of  water.  As 
one  rides  along  in  an  automobile  ascending  an  in- 
cline, if  he  closely  observes  at  the  moment  the  line 
of  sight  is  just  on  the  level  of  the  pavement,  he  will 
often  be  rewarded  by  the  sight  of  a  mirage.  An 
approaching  pedestrian  may  have  no  feet  (they  are 
replaced  by  a  bit  of  sky)  and  the  distant  pavement 
will  appear  to  contain  pools  of  water  on  its  surface. 

Sometimes  on  deserts,  over  ice  fields,  or  on  northern 
seas,  mirages  are  of  the  inverted  type.  A  horseman 
or  ship  may  appear  suspended  in  the  air  in  an  in- 
verted position.  When  the  density  of  the  air  is  great 
enough  so  that  only  the  upper  rays  reach  the  eye, 
the  object  will  be  seen  inverted  and  far  bove  the 
surface  upon  which  nothing  is  seen.  Many  modifi- 
cations of  these  types  are  possible  through  varia- 
tions in  the  refractive  indices  of  various  strata  of  air. 
Sometimes  the  air  is  stratified  horizontally  and  even 
vertically,  which  results  in  magnification  as  well  as 
other  peculiar  effects. 

As  one  rides  over  the  desert  in  a  rapidly  moving 
train  or  automobile  these  vagaries  of  nature  are  some- 
times very  striking,  because  the  speed  of  motion  will 
make  the  effects  of  the  varying  refractive  indices 
more  marked.  A  distant  foothill  may  appear  to 
float  in  the  air  or  to  change  its  shape  very  rapidly. 
An  island  surrounded  by  quiet  air  and  water  may 
appear  like  a  huge  mushroom  barely  supported  by  a 
stem. 


178  VISUAL  ILLUSIONS 

Arctic  mirages  are  no  less  wonderful  than  those 
of  the  hot  barren  deserts.  While  traveling  along 
over  the  ice  and  snow  distant  white  peaks  may  assume 
the  most  fantastic  shapes.  At  first  they  may  appear 
flattened  like  a  table-land  and  then  suddenly  they 
may  stretch  upward  like  spires.  They  may  shrink 
then  spread  like  huge  mushrooms  supported  by  the 
stalk-like  bases  and  stretching  out  laterally.  Sud- 
denly they  may  shoot  upward  into  another  series  of 
pinnacles  as  if  another  range  had  suddenly  arisen. 
Such  antics  may  go  on  for  hours  as  one  travels  along 
a  frozen  valley.  Even  a  change  of  position  of  the 
eyes  accompanying  a  change  from  erect  to  lying 
down  may  cause  remarkable  contortions  of  the  dis- 
tant mountains  and  one  is  reminded  of  the  psalmist's 
query,  "  Why  hop  ye  so,  ye  hills?  " 

Although  not  an  illusion  but  a  physical  reality,  it 
is  of  interest  in  passing  to  note  the  colored  halo  or 
aureole  surrounding  the  shadows  of  objects  cast  by 
the  sun  against  a  cloud,  fog,  or  jet  of  steam.  The 
most  wonderful  effects  are  seen  by  the  aerial  traveler 
over  a  bank  of  clouds  when  the  upper  sky  is  clear. 
For  example,  the  shadow  of  the  aircraft  cast  by  the 
sun  upon  a  dense  layer  of  clouds  is  surrounded  by 
a  halo  or  aureole  of  the  colors  of  the  rainbow.  The 
phenomenon  is  purely  optical,  involving  diffraction 
of  light.  A  well-known  example  of  this  is  the  "  Spectre 
of  the  Brocken." 


XII 
PAINTING  AND  DECORATION 

IN  the  arts  where  colors,  brightnesses,  contrasts, 
lines,  forms,  and  perspectives  mean  so  much,  it 
is  obvious  that  visual  illusions  are  important. 
Sometimes  they  are  evils  which  must  be  suppressed; 
in  some  cases  they  are  boons  to  the  artist  if  he  is  equal 
to  the  task  of  harnessing  them.  Ofttimes  they  appear 
unheralded  and  unexpected.  The  existence  of  visual 
illusions  is  sufficient  to  justify  the  artist's  pride  in 
his  "  eye  "  and  his  dependence  upon  his  visual  judg- 
ment rather  than  upon  what  he  knows  to  be  true. 
However  true  this  may  be,  knowledge  is  as  useful 
to  the  artist  as  to  anyone  else.  The  artist,  if  he  is 
to  produce  art,  is  confronted  with  the  tremendous 
task  of  perfecting  an  imperfect  nature  and  he  is  handi- 
capped with  tools  inferior  to  those  which  nature  has 
at  her  disposal.  He  must  deal  with  reflected  lights 
from  earthly  materials.  Nature  has  these  besides 
the  great  primary  light-sources  —  the  sun,  the  moon, 
the  stars,  and,  we  might  say,  the  sky.  She  also  has 
the  advantage  of  overwhelming  magnitudes. 

These  are  only  a  few  of  the  disadvantages  under 
which  the  artist  works,  but  they  indicate  that  he  must 
grasp  any  advantage  here  and  there  which  he  may. 
Knowledge  cannot  fail  him;  still,  if  he  fears  that 
it  will  take  him  out  of  his  "  dream  world  "  and  taint 

179 


180  VISUAL  ILLUSIONS 


him  with  earthliness,  let  him  ponder  over  da  Vinci, 
Rembrandt,  and  such  men.  These  men  knew  many 
things.  They  possessed  much  knowledge  and,  after 
all,  the  latter  is  nothing  more  nor  less  than  science 
when  its  facts  are  arranged  in  an  orderly  manner. 
If  the  arts  are  to  speak  "  a  noble  and  expressive 
language  "  despite  the  handicaps  of  the  artist,  knowl- 
edge cannot  be  drawn  upon  too  deeply. 

Perhaps  in  no  other  art  are  the  workmen  as  little 
acquainted  with  their  handicaps  and  with  the  scientific 
facts  which  would  aid  them  as  in  painting.  Painters, 
of  course,  may  not  agree  as  to  this  statement,  but  if 
they  wish  to  see  how  much  of  the  science  of  light, 
color,  lighting,  and  vision  they  are  unacquainted 
with,  let  them  invade  the  book-shelves.  If  they  think 
they  know  the  facts  of  nature  let  them  paint  a  given 
scene  and  then  inquire  of  the  scientist  regarding 
the  relative  values  (brightnesses)  in  the  actual  scene. 
They  will  usually  be  amazed  to  learn  that  they  cannot 
paint  the  lights  and  shadows  of  nature  excepting  in 
the  feeblest  manner.  The  range  of  contrast  repre- 
sented by  their  entire  palette  is  many  thousand 
times  less  than  the  range  of  values  in  nature.  In 
fact  exclusive  of  nature's  primary  light-sources,  such 
as  the  sun,  she  sometimes  exhibits  a  range  of  bright- 
ness in  a  landscape  a  million  times  greater  than  the 
painter  can  produce  with  black  and  white  pigments. 
This  suggests  that  the  artist  is  justified  in  using  any 
available  means  for  overcoming  the  handicap  and 
among  his  tools,  visual  illusions  are  perhaps  the  most 
powerful. 

A  painting  in  the  broadest  sense  is  an  illusion, 


PAINTING  AND   DECORATION  181 

for  it  strives  to  present  the  three-dimensional  world 
upon  plane  areas  of  two  dimensions.  Through  rep- 
resentation or  imitation  it  creates  an  illusion.  If  the 
artist's  sensibility  has  been  capable  of  adequate 
selection,  his  art  will  transmit,  by  means  of  and 
through  the  truths  of  science,  from  the.  region  of  per- 
ception to  the  region  of  emotion.  Science  consists  of 
knowing ;  art  consists  of  doing.  If  the  artist  is  familiar 
with  the  facts  of  light,  color,  lighting,  and  vision,  he 
will  possess  knowledge  that  can  aid  him  in  over- 
coming the  great  obstacles  which  are  ever-present. 
A  glimpse  of  visual  illusions  should  strengthen  him 
in  his  resolution  to  depend  upon  visual  perception, 
but  he  can  utilize  these  very  illusions.  He  can 
find  a  use  for  facts  as  well  as  anyone.  Facts  as 
well  as  experience  will  prepare  him  to  do  his  work 
best. 

The  artist  may  suggest  brilliant  sunlight  by  means 
of  deep  shadow.  The  old  painters  gained  color  at 
the  expense  of  light  and  therefore  lowered  the 
scale  of  color  in  their  representations  of  nature.  It 
is  interesting  to  see  how  increasing  knowledge,  as 
centuries  passed,  directed  painters  as  it  did  others 
onward  toward  the  truth.  Turner  was  one  of  the 
first  to  abandon  the  older  methods  in  an  attempt 
to  raise  the  scale  of  his  paintings  toward  a  brilliance 
more  resembling  nature.  By  doing  this  he  was  able 
to  put  color  in  shadows  as  well  as  in  lights.  Gradu- 
ally paintings  became  more  brilliant.  Monet,  Claude, 
and  others  worked  toward  this  goal  until  the  bright- 
nesses of  paintings  reached  the  limits  of  pigments. 
The  impressionists,  in  their  desire  to  paint  nature's 


182  VISUAL  ILLUSIONS 

light,  introduced  something  which  was  nothing  more 
nor  less  than  science.  All  this  time  the  true  creative 
artist  was  introducing  science  —  in  fact,  illusions  — 
to  produce  the  perfect  illusion  which  was  his  goal. 
A  survey  of  any  representative  paintings'  gallery 
shows  the  result  of  the  application  of  more  and  more 
knowledge,  as  the  art  of  painting  progressed  through 
the  centuries.  Surely  we  cannot  go  back  to  the  brown 
shadows  and  sombre  landscapes  of  the  past. 

In  the  earliest  art,  in  the  efforts  of  children,  in  the 
wall-paintings  of  the  Egyptians,  and  in  Japanese 
representation  of  nature,  the  process  is  selective  and 
not  imitative.  Certain  things  are  chosen  and  every- 
thing else  is  discarded.  In  such  art  selection  is  carried 
to  the  extreme.  Much  of  this  simplicity  was  due 
to  a  lack  of  knowledge.  Light  and  shade,  or  shading, 
was  not  introduced  until  science  discovered  and 
organized  its  facts.  Quite  in  the  same  manner  linear 
and  aerial  perspective  made  their  appearances  until 
in  our  present  art  the  process  of  selection  is  complex. 
In  our  paintings  of  today  objects  are  modeled  by 
light  and  shade;  they  are  related  by  perspective; 
backgrounds  and  surroundings  are  carefully  con- 
sidered; the  proper  emphasis  of  light,  shade  and 
color  are  given  to  certain  details.  The  present  com- 
plexity provides  unprecedented  opportunities  for  the 
application  of  knowledge  pertaining  to  illusions  but 
it  should  be  understood  that  this  application  tends 
only  toward  realism  of  external  things.  Idealism  in 
art  and  realism  of  character  and  expression  are  ac- 
complished by  the  same  tools  —  pigments  and  brushes 
—  as  realism  of  objective  details  is  attained  and 


PAINTING  AND  DECORATION  183 

there  is  nothing  mysterious  in  the  masterpieces 
of  this  kind.  Mystery  in  art  as  in  other  activities 
is  merely  lack  of  understanding  due  to  inadequate 
knowledge.  Mysteries  of  today  become  facts  to- 
morrow. Science  moves  with  certainty  into  the  un- 
known, reaping  and  binding  the  facts  and  dropping 
them  behind  where  they  may  be  utilized  by  those  who 
will. 

The  painter  can  imitate  aerial  perspective  al- 
though many  centuries  elapsed  before  mankind  was 
keen  enough  to  note  its  presence  in  nature.  The 
atmospheric  haze  diminishes  the  brightness  of  very 
bright  objects  and  increases  that  of  dark  objects.  It 
blurs  the  distant  details  and  adds  a  tinge  of  blue  or 
violet  to  the  distance.  In  painting  it  is  a  powerful 
illusion  which  the  painter  has  learned  to  employ. 

The  painter  can  accurately  imitate  mathematical 
or  linear  perspective  but  the  art  of  early  centuries  does 
not  exhibit  this  feature.  In  a  painting  a  tremendously 
powerful  illusion  of  the  third  dimension  is  obtained 
by  diminishing  the  size  of  objects  as  they  are  rep- 
resented in  the  distance.  Converging  lines  and  the 
other  manifold  details  of  perspective  are  aiding  the 
artist  in  his  efforts  toward  the  production  of  the  great 
illusion  of  painting. 

The  painter  cannot  imitate  focal  perspective  or 
binocular  perspective.  He  can  try  to  imitate  the 
definition  in  the  central  portion  of  the  visual  field 
and  the  increased  blurring  toward  the  periphery. 
Focal  perspective  is  not  of  much  importance  in  paint- 
ing, because  it  is  scarcely  perceptible  at  the  distances 
at  which  paintings  are  usually  viewed.  However 


184  VISUAL  ILLUSIONS 

the  absence  of  binocular  perspective  in  painting  does 
decrease  the  effectiveness  of  the  illusion  very  markedly. 
For  this  reason  a  painting  is  a  more  successful  illu- 
sion when  viewed  with  one  eye  than  with  two  eyes. 
Of  course,  in  one  of  nature's  scenes  the  converse  is 
true  because  when  viewing  it  with  both  eyes  all  the 
forms  of  perspective  cooperate  to  the  final  end  — 
the  true  impression  of  three  dimensions. 

The  painter  may  imitate  the  light  and  shade  of 
solid  forms  and  thereby  apparently  model  them.  In 
this  respect  a  remarkable  illusion  of  solid  form  or  of 
depth  may  be  obtained.  For  example,  a  painted  col- 
umn may  be  made  to  appear  circular  in  cross-section 
or  a  circle  when  properly  shaded  will  appear  to  be  a 
sphere.  Both  of  these,  of  courseware  pure  illusions. 
Some  stage  paintings  are  remarkable  illusions  of 
depth,  and  their  success  depends  chiefly  upon  linear 
perspective  and  shadows.  However,  the  illusion  which 
was  so  complete  at  a  distance  quite  disappears  at 
close  range. 

The  inadequate  range  of  brightnesses  or  values 
obtainable  by  means  of  pigments  has  already  been 
discussed.  The  sky  in  a  landscape  may  be  thousands 
of  times  brighter  than  a  deep  shadow  or  a  hole  in  the 
ground.  A  cumulus  cloud  in  the  sky  may  be  a  hundred 
thousand  times  brighter  than  the  deepest  shadow. 
However,  the  artist  must  represent  a  landscape  by 
means  of  a  palette  whose  white  is  only  about  thirty 
times  brighter  than  its  black.  If  the  sun  is  considered 
we  may  have  in  a  landscape  a  range  of  brightness 
represented  by  millions. 

This  illustrates  the  pitiable  weakness  of  pigments 


PAINTING  AND  DECORATION  185 

alone  as  representative  media.  Will  not  light  trans- 
mitted through  media  some  day  be  utilized  to  over- 
come this  inherent  handicap  of  reflecting  media?  To 
what  extent  is  the  success  of  stained  glass  windows 
due  to  a  lessening  of  this  handicap?  The  range  of 
brightness  in  this  case  may  be  represented  by  a  black 
(non-transmitting)  portion  to  the  brightness  of  the 
background  (artificial  or  sky)  as  seen  through  an 
area  of  clear  glass.  Transparencies  have  an  inherent 
advantage  over  ordinary  paintings  in  this  respect 
and  many  effective  results  may  be  obtained  with  them 
even  in  photography. 

It  is  interesting  to  study  the  effect  of  greatly  in- 
creasing the  range  of  values  or  brightnesses  in  paint- 
ings by  utilizing  non-uniform  distributions  of  light. 
Let  us  take  a  given  landscape  painting.  If  a  light- 
source  be  so  placed  that  it  is  close  to  the  brighter 
areas  (perhaps  clouds  and  sky  near  the  sun)  it  will 
illuminate  this  brighter  portion  several  times  more 
intensely  than  the  more  distant  darker  portions  of 
the  picture  (foreground  of  trees,  underbrush,  deep 
shadows,  etc.).  The  addition  to  the  effectiveness  of 
the  illusion  is  quite  perceptible.  This  effect  of  non- 
uniform  lighting  may  be  carried  to  the  extreme  for 
a  painting  by  making  a  positive  lantern-slide  (rather 
contrasty)  of  the  painting  and  projecting  this  slide 
upon  the  painting  in  accurate  superposition.  Now  if 
the  painting  is  illuminated  solely  by  the  "  lantern- 
slide  "  the  range  of  contrast  or  brightness  will  be 
enormously  increased.  The  lightest  portions  of  the 
picture  will  now  be  illuminated  by  light  passing  through 
the  almost  totally  transparent  portions  of  the  slide 


186  VISUAL  ILLUSIONS 

and  the  darkest  portions  by  light  greatly  reduced  by 
passing  through  the  nearly  opaque  portions  of  the  slide. 
The  original  range  of  contrast  in  the  painting,  per- 
haps twenty  to  one,  is  now  increased  perhaps  to  more 
than  a  thousand  to  one.  This  demonstration  will  be 
surprising  to  anyone  and  will  emphasize  a  very  im- 
portant point  to  the  painter. 

The  painter  has  at  his  disposal  all  the  scientific 
facts  of  light,  color,  and  vision.  Many  of  these  have 
been  presented  elsewhere,9  and  those  pertaining  to 
illusions  have  been  discussed  in  preceding  chapters. 
These  need  not  be  repeated  here  excepting  a  few 
for  the  purpose  of  reminding  the  reader  of  the  wealth 
of  material  available  to  the  painter  and  decorator. 
Many  tricks  may  be  interjected  into  the  foreground 
for  their  effect  upon  the  background  and  vice  versa. 
For  example,  a  branch  of  a  tree  drooping  in  the  fore- 
ground apparently  close  to  the  observer,  if  done  well, 
will  give  a  remarkable  depth  to  a  painting.  Modeling 
of  form  may  be  effected  to  some  extent  by  a  judicious 
use  of  the  "  retiring  "  and  "  advancing  "  colors.  This 
is  one  way  to  obtain  the  illusion  of  depth. 

After-images  play  many  subtle  parts  in  painting. 
For  example,  in  a  painting  where  a  gray-blue  sky 
meets  the  horizon  of  a  blue-green  body  of  water,  the 
involuntary  eye-movements  may  produce  a  pinkish 
line  just  above  the  horizon.  This  is  the  after-image 
of  the  blue-green  water  creeping  upward  by  eye- 
movements.  Many  vivid  illusions  of  this  character 
may  be  deliberately  obtained  by  the  artist.  Some 
of  the  peculiar  restless  effects  obtained  in  impres- 
sionistic painting  (stippling  of  small  areas  with  rela- 


PAINTING  AND  DECORATION  187 

tively  pure   hues)   are   due   to   contrasts   and  after- 
images. 

A  painting  came  to  the  author's  notice  in  which 
several  after-images  of  the  sun,  besides  the  image 
of  the  sun  itself,  were  disposed  in  various  positions. 
Their  colors  varied  in  the  same  manner  as  the  after- 
image of  the  sun.  Doubtless  the  painter  strove  to 
give  the  impression  which  one  has  on  gazing  at  the 
sun.  Whether  or  not  this  attempt  was  successful 
does  not  matter  but  it  was  gratifying  to  see  the  attempt 
made. 

There  are  many  interesting  effects  obtainable  by 
judicious  experimentation.  For  example,  if  a  gray 
medium  be  sprayed  upon  a  landscape  in  such  a  manner 
that  the  material  dries  in  a  very  rough  or  diffusing 
surface  some  remarkable  effects  of  fog  and  haze 
may  be  produced.  While  experimenting  in  this 
manner  a  very  finely  etched  clear  glass  was  placed 
over  a  landscape  and  the  combined  effect  of  dif- 
fusely reflected  light  and  of  the  slight  blurring  was 
remarkable.  By  separating  the  etched  glass  from 
the  painting  a  slight  distance,  a  very  good  imitation 
"  porcelain  "  was  produced.  The  optical  properties 
of  varnishes  vary  and  their  effect  varies  considerably, 
depending  upon  the  mode  of  application.  These  and 
many  other  details  are  available  to  the  painter  and 
decorator.  An  interesting  example  among  many  is 
a  cellulose  lacquer  dyed  with  an  ordinary  yellow  dye. 
The  solution  appears  yellow  by  transmitted  light 
or  it  will  color  a  surface  yellow.  By  spraying  this 
solution  on  a  metallic  object  such  as  a  nickel-plated 
piece,  in  a  manner  that  leaves  the  medium  rough 


188  VISUAL  ILLUSIONS 

or  diffusing,  the  effect  is  no  longer  merely  a  yellow 
but  a  remarkable  lustre  resembling  gilt.  Quite  in 
the  same  manner  many  effects  of  richness,  depth 
of  color,  haziness,  etc.,  are  obtainable  by  the  artist 
who  is  striving  to  produce  a  great  illusion. 

All  the  means  for  success  which  the  painter  pos- 
sesses are  also  available  to  the  decorator;  however, 
the  latter  may  utilize  some  of  the  illusions  of  line, 
form,  irradiation,  etc.,  which  the  architect  encounters. 
The  decorator's  field  may  be  considered  to  include 
almost  all  of  the  painter's  and  much  of  the  architect's. 
This  being  the  case,  little  space  will  be  given  to  this 
phase  of  the  subject  because  painting  and  architecture 
are  separately  treated.  The  decorator  should  begin 
to  realize  more  fully  the  great  potentiality  of  lighting 
in  creating  moods  or  in  giving  expression  to  an  in- 
terior. The  psychology  of  light  and  the  use  of  lighting 
as  a  mode  of  expression  have  barely  been  drawn 
upon  by  the  decorator.  Lighting  has  already  been 
discussed  so  it  will  be  passed  by  at  this  point. 

The  practice  of  hanging  pictures  on  walls  which 
are  brilliantly  colored  is  open  to  criticism.  There 
are  galleries  in  existence  where  paintings  are  hung 
on  brilliant  green  or  rose  walls.  The  changes  in  the 
appearance  of  the  object  due  to  these  highly  colored 
environments  are  easily  demonstrated  by  viewing 
a  piece  of  white  paper  pinned  upon  the  wall.  On  the 
green  wall,  the  white  paper  appears  pinkish;  on  the 
rose  wall,  it  appears  bluish  or  greenish.  A  portrait 
or  a  picture  in  which  there  are  areas  of  white  or  delicate 
tints  is  subject  to  considerable  distortions  in  the 
appearance  of  its  colors.  Similarly,  if  a  woman  must 


PAINTING  AND  DECORATION  189 

have  a  colored  background,  it  is  well  to  choose  one 
which  will  induce  the  more  desirable  tints  in  her  ap- 
pearance. The  designer  of  gowns  certainly  must 
recognize  these  illusions  of  color  which  may  be  desir- 
able or  undesirable. 

The  lighting  of  a  picture  has  already  been  men- 
tioned, but  the  discussion  was  confined  solely  to 
distribution  of  light.  The  quality  of  the  light  (its 
spectral  character)  may  have  an  enormous  influence 
upon  the  painting.  In  fact  with  the  same  painting 
many  illusions  may  be  produced  by  lighting.  In 
general,  paintings  are  painted  in  daylight  and  they 
are  not  the  same  in  appearance  under  ordinary  arti- 
ficial light.  For  this  reason  the  artist  is  usually  entitled 
to  the  preservation  of  the  illusion  as  he  completed 
it.  By  using  artificial  daylight  which  has  been  avail- 
able for  some  years,  the  painting  appears  as  the 
artist  gave  it  his  last  touch.  Of  course,  it  is  quite 
legitimate  to  vary  the  quality  of  light  in  case  the 
owner  desires  to  do  so,  but  the  purpose  here  is  to 
emphasize  the  fact  that  the  quality  of  light  is  a  power- 
ful influence  upon  the  appearance  of  the  painting. 
The  influence  is  not  generally  enough  recognized  and 
its  magnitude  is  appreciated  by  relatively  few  persons. 

All  other  considerations  aside,  a  painting  is  best 
hung  upon  a  colorless  background  and  black  velvet 
for  this  purpose  yields  remarkable  results.  Gray 
velvet  is  better,  when  the  appearance  of  the  room  is 
taken  into  consideration,  as  it  must  be.  However, 
the  influence  of  dark  surroundings  toward  enhancing 
the  illusion  is  well  worth  recognizing.  In  the  case  of 
a  special  picture  or  a  special  occasion,  a  painting  may 


190 


VISUAL  ILLUSIONS 


be  exhibited  in  a  booth  —  a  huge  shadow-box  not 
unlike  a  show-window  in  which  the  light-sources  are 
concealed.  Such  experiments  yield  many  interesting 
data  pertaining  to  the  illusions  which  the  painter 
strives  to  obtain. 

Incidentally  on  viewing  some  picture  frames  in 
which  the  grain  of  the  wood  was  noticeable,  the  frames 


Fig.  82.  —  Illustrating  the  apparent  distortion  of  a  picture  frame  in  which 
the  grain  of  the  wood  is  visible. 


did  not  appear  to  be  strictly  rectangular.  The  illusions 
were  so  strong  that  only  by  measuring  the  frames 
could  one  be  convinced  that  they  were  truly  rect- 
angular and  possessed  straight  sides.  Two  of  these 
are  represented  in  Figs.  82  and  83.  In  the  former, 
the  horizontal  sides  appear  bent  upward  in  the  middle 
and  the  two  vertical  sides  appear  bowed  toward  the 
right.  In  Fig.  83,  the  frame  appears  considerably 
narrower  at  the  left  end  than  at  the  right.  Both  these 
frames  were  represented  in  the  original  drawings 
by  true  rectangles. 


PAINTING  AND  DECORATION 


191 


Many  illusions  are  to  be  seen  in  furniture  and 
in  other  woodwork  in  which  the  grain  is  conspicuous. 
This  appears  to  the  author  to  be  an  objection  in  general 
to  this  kind  of  finish.  In  Fig.  84  there  is  reproduced 
a  photograph  of  the  end  of  a  board  which  was  plane 
or  straight  notwithstanding  its  warped,  or  bowed, 
appearance.  The  original  photographs  were  placed 


Fig.  83.  —  Another  example  similar  to  Fig.  82. 

so  as  to  be  related  as  shown  in  the  figure.  Various 
degrees  of  the  illusion  are  evident.  The  reader  will 
perhaps  find  it  necessary  to  convince  himself  of  the 
straightness  of  the  horizontal  edges  by  applying  a 
straight  edge.  These  are  examples  of  the  same 
illusion  as  shown  in  Figs.  37  to  40. 

Perhaps  a  brief  statement  regarding  the  modern 
isms  in  art  may  be  of  interest.  In  considering  some 
of  the  extreme  examples,  we  must  revise  our  idea  that 
art  is  or  should  be  always  beautiful.  The  many 
definitions  of  art  would  lead  us  too  far  afield  to  dis- 
cuss them  here  but  in  its  most  extended  and  popular 


192 


VISUAL  ILLUSIONS 


Fig.  84.  —  From  actual  photographs  of  the  end-grain  of  a  board. 


PAINTING  AND  DECORATION  193 

sense,  art  may  be  considered  to  mean  everything 
which  we  distinguish  from  nature.  Certainly  art  need 
not  be  beautiful,  although  it  does  seem  that  the  world 
would  welcome  the  beautiful  and  would  get  along 
contentedly  without  art  that  is  ugly  or  repulsive. 
The  modern  isms  must  be  viewed  with  consideration, 
for  there  are  many  impostors  concealing  their  inabili- 
ties by  flocking  to  these  less  understood  fields.  How- 
ever, there  are  many  sincere  workers  —  research 
artists  —  in  the  modern  isms  and  their  works  may 
best  be  described  at  present  as  experiments  in  the 
psychology  of  light,  shade,  and  color.  They  have 
cast  aside  or  reduced  in  importance  some  of  the 
more  familiar  components  such  as  realism  and  are 
striving  more  deeply  to  utilize  the  psychology  of  light 
and  color.  Some  of  them  admit  that  they  strive  to 
paint  through  child's  eyes  and  mind  —  free  from 
experience,  prejudice,  and  imitation.  These  need 
all  the  scientific  knowledge  which  is  available  —  and 
maybe  more. 

In  closing  this  chapter,  it  appears  necessary  to 
remind  the  artist  and  others  that  it  is  far  from  the 
author's  intention  to  subordinate  the  artist's  sensi- 
bility to  the  scientific  facts  or  tools.  Art  cannot  be 
manufactured  by  means  of  formulae.  This  would 
not  be  true  if  we  knew  a  great  deal  more  than  we  do 
pertaining  to  the  science  of  light,  color,  and  vision. 
The  artist's  fine  sensibility  will  always  be  the  domi- 
nating necessity  in  the  production  of  art.  He  must 
possess  the  ability  to  compose  exquisitely;  he  must 
be  able  to  look  at  nature  through  a  special  tempera- 
ment; he  must  be  gifted  in  eye  and  in  hand;  he 


194  VISUAL  ILLUSIONS 

v 
must  be  master  of  unusual  visual  and  intellectual 

processes.  But  knowledge  will  aid  him  as  well  as 
those  in  other  activities.  A  superior  acquaintance 
with  scientific  facts  lifted  past  masters  above  their 
fellows  and  what  helped  Leonardo  da  Vinci,  Rem- 
brandt, Velasquez,  Turner,  Claude,  Monet,  and  other 
masters  will  help  artists  of  today.  What  would  not 
those  past  masters  have  accomplished  if  they  had 
available  in  their  time  the  greater  knowledge  of  the 
present! 


M 


XIII 
ARCHITECTURE 

'ANY  illusions  are  found  in  architecture  and, 
strangely  enough,  many  of  these  were  recog- 
nized long  before  painting  developed  beyond 
its  primitive  stages.  The  architecture  of  classic 
Greece  displays  a  highly  developed  knowledge  of 
many  geometrical  illusions  and  the  architects  of 
those  far-off  centuries  carefully  worked  out  details 
for  counteracting  them.  Drawings  reveal  many  il- 
lusions to  the  architect,  but  many  are  not  predicted 
by  them.  The  ever-changing  relations  of  lines  and 
forms  in  architecture  as  we  vary  our  viewpoint  in- 
troduce many  illusions  which  may  appear  and  dis- 
appear. No  view  of  a  group  of  buildings  or  of  the 
components  of  a  single  structure  can  be  free  from 
optical  illusions.  We  never  see  in  the  reality  the 
same  relations  of  lines,  forms,  colors,  and  bright- 
nesses as  indicated  by  the  drawings  or  blue-prints. 
Perhaps  this  is  one  of  the  best  reasons  for  justifying 
the  construction  of  expensive  models  of  our  more 
pretentious  structures. 

No  detailed  account  of  the  many  architectural 
illusions  will  be  attempted,  for  it  is  easy  for  the  reader 
to  see  many  of  the  possibilities  suggested  by  preceding 
chapters.  However,  a  few  will  be  touched  upon  to 
reveal  the  magnitude  of  the  illusory  effect  and  to 

195 


196  VISUAL  ILLUSIONS 

aid  the  observer  in  looking  for  or  recognizing  them, 
or  purely  for  historical  interest.  In  architecture  the 
eye  cannot  be  wholly  satisfied  by  such  tools  as  the 
level,  the  square,  and  the  plumb-line.  The  eye  is 
satisfied  only  when  the  appearance  is  satisfactory. 
For  the  purpose  of  showing  the  extent  of  certain  archi- 
tectural illusions,  the  compensatory  measures  ap- 
plied by  the  Greeks  are  excellent  examples.  These 
also  reveal  the  remarkable  application  of  science 
to  architecture  as  compared  with  the  scanty  applica- 
tion in  painting  of  the  same  period. 

During  the  best  period  of  Grecian  art  many  refine- 
ments were  applied  in  order  to  correct  optical  illu- 
sions. It  would  be  interesting  to  know  to  what  extent 
the  magnitude  of  the  illusions  as  they  appeared  to 
many  persons  were  actually  studied.  The  Parthe- 
non of  Athens  affords  an  excellent  example  of  the 
magnitude  of  the  corrections  which  the  designer 
thought  necessary  in  order  to  satisfy  the  eye.  The 
long  lines  of  the  architrave  —  the  beam  which  sur- 
mounts the  columns  or  extends  from  column  to  column 
—  would  appear  to  sag  if  it  were  actually  straight. 
This  is  also  true  of  the  stylobate,  or  substructure 
of  a  colonnade,  and  of  pediments  and  other  features. 
These  lines  were  often  convex  instead  of  being  straight 
as  the  eye  desires  to  see  them. 

In  the  Parthenon,  the  stylobate  has  an  upward 
curvature  of  more  than  four  inches  on  the  sides  of 
the  edifice  and  of  more  than  two  and  a  half  inches 
on  the  east  and  west  fronts.  Vertical  features  were 
made  to  incline  inward  in  order  to  correct  the  com- 
mon appearance  of  leaning  outward  at  the  top.  In 


ARCHITECTURE  197 


the  Parthenon,  the  axes  of  the  columns  are  not  vertical, 
but  they  are  inclined  inward  nearly  three  niches. 
They  are  said  also  to  be  inclined  toward  each  other 
to  such  a  degree  that  they  would  meet  at  an  altitude 
of  one  mile  above  the  ground.  The  eleven-foot  frieze 
and  architrave  is  inclined  inward  about  one  and 
one-half  inches. 

In  Fig.  85,  a  represents  the  front  of  a  temple  as 
it  should  appear;  b  represents  its  appearance  (ex- 
aggerated) if  it  were  actually  built  like  a  without 
compensations  for  optical  illusions;  c  represents  it  as 
built  and  showing  the  physical  corrections  (exagger- 
ated) in  order  that  it  may  appear  to  the  eye  as  a  does. 

Tall  columns  if  they  are  actually  straight  are  likely 
to  appear  somewhat  shrunken  in  the  middle;  there- 
fore they  are  sometimes  made  slightly  swollen  in 
order  to  appear  straight.  This  outward  curvature  of 
the  profile  is  termed  an  entasis  and  in  the  Parthenon 
column,  which  is  thirty-four  feet  in  height,  amounted 
to  about  three-fourths  of  an  inch.  In  some  early 
Grecian  works,  it  is  said  that  this  correction  was  over- 
done but  that  its  omission  entirely  is  quite  unsatis- 
factory. Some  authorities  appear  to  believe  that 
an  excellent  compromise  is  found  in  the  Parthenon 
columns. 

One  of  the  conditions  which  is  responsible  for 
certain  illusions  and  has  been  compensated  for  on 
occasions  is  represented  in  Fig.  86.  On  the  left  are 
a  series  of  squares  of  equal  size  placed  in  a  vertical 
row.  If  these  are  large  so  that  they  might  represent 
stories  in  a  building  they  will  appear  to  decrease  in 
size  from  the  bottom  upward,  because  of  the  decreas- 


198 


VISUAL  ILLUSIONS 


!          i          i 

Fig.  86.  —  Exaggerated  illusions  in  architecture. 


ARCHITECTURE 


199 


ing  projection  at  the  eye.  This  is  obvious  if  the  eye 
is  considered  to  be  at  the  point  where  the  inclined 
lines  meet.  In  order  to  compensate  for  the  variation 
in  visual  angle,  there  must  be  a  series  of  rectangles 
increasing  considerably  in  height  toward  the  top.  The 
correction  is  shown  in  the  illustration.  It  is  stated 


Fig.  86.  —  Illustrating  the  influence  of  visual  angle  upon  apparent 
vertical  height. 


that  an  inscription  on  an  ancient  temple  was  written 
in  letters  arranged  vertically,  and  in  order  to  make 
them  appear  of  equal  size  they  were  actually  in- 
creased in  size  toward  the  top  according  to  the  law 
represented  in  Fig.  86.  Obviously  a  given  correction 
would  be  correct  only  for  one  distance  in  a  given 
plane. 

In  Chapter  VIII  the  phenomenon  of  irradiation 
was  discussed  and  various  examples  were  presented. 
It  exerts  its  influence  in  the  arts  as  elsewhere.  Col- 
umns viewed  against  a  background  of  white  sky 


200  VISUAL  ILLUSIONS 

appear  of  smaller  diameter  than  when  they  are  viewed 
against  a  dark  background.  This  is  illustrated  in 
Fig.  87  where  the  white  and  the  black  columns  are 
supposed  to  be  equal  in  diameter. 

The  careful  observer  will  find  numberless  optical 
illusions  and  occasionally  he  will  recognize  an  at- 
tempt on  the  part  of  the  architect  to  apply  an  illusory 
effect  to  his  advantage.  In  Fig.  88  some  commonplace 
illusions  are  presented,  not  for  what  they  are  worth, 


Fig.  87.  —  Irradiation  in  architecture. 

but  to  suggest  how  prevalent  they  may  be.  Where 
the  pole  or  column  intersects  the  arches  or  circle, 
there  is  an  apparent  change  in  the  direction  of  the 
curved  lines.  The  different  types  of  arches  show 
different  degrees  of  the  illusion.  It  may  be  of  in- 
terest for  the  reader  to  refer  to  preceding  chapters 
and  to  ascertain  what  types  of  illusions  are  involved. 

If  a  high  wall  ends  in  a  series  of  long  horizontal 
steps  at  a  slightly  inclined  sidewalk,  the  steps  are 
not  likely  to  appear  horizontal. 

Some  remarkable  illusions  of  depth  or  of  solid 
form  are  given  to  flat  surfaces  when  snow  is  driven 
against  them  so  as  to  adhere  in  decreasing  amounts 
similar  to  shading. 

A  suggestion  of  augmented  height  may  be  given 


ARCHITECTURE 


201 


to  a  low  tower  by  decreasing  the  size  of  its  successive 
portions  more  rapidly  than  demanded  by  perspective 
alone.  The  same  principal  can  be  applied  in  many 
ways.  For  example,  in  Fig.  89  the  roof  appears  quite 
extensive  when  viewed  so  that  the  end-walls  of  the 
structure  are  not  seen.  Such  illusions  find  applications 


Fig.  88.  —  Some  simple  geometrical-optical  illusions  in  architecture. 

in  the  moving-picture  studio  where  extensive  interiors, 
great  fortresses,  and  even  villages  must  be  erected 
within  small  areas.  Incidentally  the  camera  aids  to 
create  the  illusion  of  magnitude  in  photographs 
because  it  usually  magnifies  perspective,  thereby 
causing  scenes  to  appear  more  extensive  in  the  photo- 
graphs than  in  the  reality. 

Balance  in  architecture  is  subject  to  illusions  and 
might  be  considered  an  illusion  itself.  For  example, 
our  judgment  of  balance  is  based  largely  upon  mechan- 
ical laws.  A  composition  must  appear  to  be  stable; 
that  is,  a  large  component  such  as  a  tower  must  not 
be  situated  too  far  from  what  we  take  as  a  center  of 


202 


VISUAL  ILLUSIONS 


gravity,  to  appear  capable  of  tipping  the  remainder 
of  the  structure.  In  physics  we  would  apply  the  term 
"  moment."  Each  mass  may  be  multiplied  by  its  dis- 
tance from  the  center  of  gravity,  thus  determining 
its  moment.  For  a  building  or  other  composition  to 
appear  stable  the  sum  of  these  moments  must  be 


Fig.  89. —  By  decreasing  the  exposed  length  of  shingles  toward  the  top 
a  greater  apparent  expanse  is  obtained. 

zero;  that  is,  those  tending  to  turn  the  figure  in  one 
direction  must  be  counterbalanced  by  those  tending 
to  turn  it  in  another  direction.  In  appraising  a  com- 
position, our  intellect  summates  the  effects  of  different 
parts  somewhat  in  this  manner  and  if  satisfactory, 
balance  is  considered  to  have  been  attained.  The 
colors  of  the  various  components  exert  an  influence 
in  this  respect,  so  it  is  seen  that  illusions  may  have 
much  to  do  with  the  satisfactoriness  of  architectural 
compositions. 


ARCHITECTURE  203 

Various  illusions  of  height,  of  ceiling,  composed- 
ness,  etc.,  may  be  obtained  by  the  color  of  the  ceiling. 
A  dark  cornice  in  an  interior  may  appear  to  be  un- 
supported if  the  walls  below  are  light  in  color,  without 
any  apparent  vertical  supports  for  the  cornice.  We 
are  then  subjected  to  the  illusion  of  instability  or 
incongruity.  Dark  beams  of  ceilings  are  not  so  ob- 
trusive because  our  intellect  tells  us  that  they  are 
supports  passing  over  the  top  of  the  walls  and  are 
therefore  able  to  support  themselves.  Color  and 
brightness  in  such  cases  are  very  important. 

The  architectural  details  on  exteriors  evolved 
under  daylighting  outdoors  so  that  their  form  has 
been  determined  by  the  shadows  desired.  The 
architect  leads  his  lights  and  shadows  around  the 
building  modeling  it  as  he  desires.  An  offset  here 
and  a  depression  there  models  the  exterior  in  light 
and  shade.  The  forms  must  be  powerful  enough  to 
resist  the  obliterating  effect  of  overcast  skies  but 
notwithstanding  all  precautions  the  expression  of  an 
exterior  varies  considerably  with  nature's  lighting. 
Indoors  the  architect  has  a  powerful  controllable 
medium  in  artificial  light  which  he  may  draw  upon 
for  producing  various  expressions  or  moods  in  rooms. 
The  effect  of  shadows  is  interesting  when  viewing 
some  structures  flood-lighted  at  night.  In  those 
cases  where  the  light  is  directed  upward  there  is  a 
reversal  of  shadows  which  is  sometimes  very  un- 
satisfactory. 

It  is  interesting  to  experiment  with  various 
ornamental  objects  lighted  from  various  directions. 
For  example,  a  Corinthian  capital  lighted  from  below 


204  VISUAL  ILLUSIONS 

may  produce  an  unpleasant  impression  upon  the 
observer.  We  do  not  like  to  have  the  dominant  light 
from  below,  perhaps  because  it  is  annoying  to  the  eyes. 
Possibly  this  is  an  instinct  acquired  by  experience 
in  snow-fields  or  on  the  desert,  or  it  may  be  a  heritage 
of  ancestral  experience  gained  under  these  glaring 
conditions.  This  dislike  manifests  itself  when  we 
appraise  shadow-effects  and  therefore  our  final  im- 
pression is  tempered  by  it. 

All  sculptured  objects  depend  for  their  appearance 
upon  the  lighting,  and  they  are  greatly  influenced  by 
it.  In  sculpture,  in  a  strict  sense,  illusions  play  a 
lesser  part  than  in  other  arts.  Perhaps  in  those  of 
very  large  proportions  various  corrections  have  been 
applied.  A  minor  detail  of  interest  is  the  small  cavity 
in  the  eye,  corresponding  to  a  reversed  cornea.  This 
depression  catches  a  shadow  which  gives  considerable 
expression  to  the  eye. 


XIV 
MIRROR  MAGIC 

STRICTLY  speaking  there  are  fewer  illusions 
found  in  the  practice  of  the  magician  than  is 
generally  supposed;  that  is,  the  eye  usually 
delivers  correctly  to  the  intellect,  but  the  judgment 
errs  for  various  reasons.  The  "  illusion  "  is  due  to 
false  assumptions,  to  the  distracting  words,  to  unduly 
accented  superfluous  movements  of  the  magician;  or 
in  general  to  downright  trickery.  Much  of  the  ma- 
gician's success  is  due  to  glibness  of  tongue  and 
deftness  of  fingers,  but  many  of  the  more  notable 
"  tricks  "  were  those  involving  the  use  of  mirrors  and 
the  control  of  light.  Black  curtains,  blackened  as- 
sistants, and  controlled  light  have  played  prominent 
parts  in  the  older  magic,  but  the  principles  of  these 
are  easily  understood.  However,  the  mirror  perhaps 
has  done  more  to  astound  the  audience  than  any  other 
device  employed  by  the  magician.  For  this  reason, 
and  because  its  effects  are  commonly  termed  illusions, 
some  representative  examples  will  be  presented. 

In  a  previous  chapter  attention  was  called  to  the 
simple  but  usually  overlooked  fact  that,  for  example, 
the  image  of  a  face  in  a  mirror  is  reversed  as  to  right 
and  left.  When  this  fact  is  overlooked  we  may  be 
astonished  at  the  changed  expression  of  an  intimate 
friend  as  we  view  the  face  (reversed)  in  the  mirror. 

205 


206  VISUAL  ILLUSIONS 

Similarly  our  own  features  are  reversed  as  to  right 
and  left  and  we  are  acquainted  with  this  reversed 
image  rather  than  the  appearance  of  our  face  as  it 
is.  Inasmuch  as  faces  are  not  accurately  symmetrical 
and  many  are  quite  unsymmetrical  the  effects  of  the 
mirror  are  sometimes  startling.  It  might  be  of  in- 
terest for  the  reader  to  study  his  face  in  the  mirror 
and  note  that  the  right  ear  is  the  left  ear  of  the  image 
which  he  sees.  He  will  also  find  it  of  interest  to  com- 
pare the  face  of  a  friend  as  viewed  directly  with  the 
appearance  of  its  image  in  the  mirror.  If  he  desires 
to  see  himself  as  others  see  him,  he  can  arrange 
two  mirrors  vertically  almost  at  a  right-angle.  By  a 
little  research  he  will  find  an  image  of  his  own  face, 
which  is  not  reversed;  that  is,  an  image  whose  right 
ear  is  really  his  right  ear. 

A  famous  "  illusion  "  which  astounded  audiences 
was  the  sphinx  illustrated  in  Fig.  90.  The  box  was 
placed  upon  a  table  and  when  opened  there  was 
revealed  a  Sphinxian  head,  but  why  it  was  called  a 
Sphinx  is  clothed  in  mystery  because  upon  some  oc- 
casions it  talked.  As  a  matter  of  fact  it  belonged  to 
a  body  which  extended  downward  from  the  table-top 
and  this  kneeling  human  being  was  concealed  from 
the  audience  by  two  very  clean  plate-glass  mirrors 
M  shown  in  the  accompanying  diagram.  The  table 
actually  appeared  to  have  three  legs  but  the  audience 
if  it  noticed  this  at  all  assumed  the  fourth  leg  was 
obscured  by  the  foremost  leg.  The  walls,  floor,  and 
ceiling  of  the  box-like  recess  in  which  the  table  was 
placed  were  covered  with  the  same  material.  It  is 
seen  by  the  diagram  that  the  mirrors  M  reflected 


MIRROR  MAGIC 


207 


images  of  the  side  walls  W  and  these  images  were 
taken  by  the  audience  to  be  portions  of  the  rear  wall 
W.    Thus  the  table  appeared  to  be  open  underneath 
and  the  possibilities  of  the  apparatus  are  evident. 
The  magician  with  a  fine  flow  of  language  could 


Fig.  90.  —  An  example  of  a  "mirror"  illusion. 

dwell  at  length  upon  the  coming  to  life  of  the  head 
of  an  ancient  statue  which  he  had  in  the  box  in  his 
hand.  Walking  to  the  table  he  could  place  the  box 
over  a  trap-door  and  by  the  time  he  had  unlatched 
the  door  of  the  box,  the  assistant  kneeling  under  the 
table  could  have  his  head  thrust  upward  through  the 
trap-door  of  the  table-top  into  the  box.  After  a  few 
impressive  words,  supposed  to  be  Hindoo  but  in  reality 
were  Hoodoo,  presto!  and  the  Sphinx  was  revealed. 


208 


VISUAL  ILLUSIONS 


It  conversed  after  a  period  of  silence  extending  back 
to  the  days  of  Rameses  when  a  wrathful  god  con- 
demned an  unfortunate  king  to  imprisonment  in  the 
stone  statue.  The  original  trick  awed  audiences  for 
many  nights  and  defied  explanation  until  one  night 
a  keen  observer  noted  finger-prints  on  what  proved 
to  be  a  mirror.  Doubtless  a  careless  accomplice  lost 


Fig.  91.  —  Another  example  of  "mirror  magic." 

his  job,  but  the  damage  had  been  done,  for  the  trick 
was  revealed.  This  "  illusion  "  is  so  effective  that 
it,  or  variations  of  it,  are  still  in  use. 

Another  simple  case  is  illustrated  in  Fig.  91.  A 
large  plate-glass  mirror  M  was  placed  at  an  angle  of 
approximately  45  degrees  from  the  floor.  Through  a 
hole  in  it  an  assistant's  head  and  shoulders  projected 
and  the  edge  of  the  opening  was  covered  with  a  draped 
cloth.  The  audience  saw  the  image  of  the  ceiling  C 
of  the  alcove  reflected  by  the  mirror  but  being  ig- 


MIRROR  MAGIC  209 


norant  of  the  presence  of  the  mirror,  assumed  this 
image  to  be  the  rear  wall.  This  trick  was  effective 
for  many  years.  Obviously  the  mirrors  must  be 
spotlessly  clean  and  the  illuminations  of  the  walls, 
ceiling,  and  in  some  cases,  the  floor  must  be  very 
uniform.  Furthermore,  no  large  conspicuous  pattern 
could  be  used  for  lining  the  box-like  recess. 

The  foregoing  examples  illustrate  the  principles 
involved  in  the  appearance  of  ghosts  on  the  stage 
and  of  a  skeleton  or  other  gruesome  object  in  place 
of  a  human  being.  The  possibilities  of  mirrors  in 
such  fields  are  endless  and  they  can  be  studied  on  a 
small  scale  by  anyone  interested.  The  pseudoscope 
which  produces  effects  opposite  to  those  of  the  stereo- 
scope is  an  interesting  device. 

The  foregoing  is  the  faintest  glimpse  of  the  use 
of  the  mirror,  but  it  does  not  appear  advisable  to  dwell 
further  upon  its  use,  for  after  all  the  results  are  not 
visual  illusions  in  the  sense  of  the  term  as  usually 
employed  throughout  this  book. 


XV 
CAMOUFLAGE 

TLLUSIONS  played  many  roles  in  the  science  and 
art  of  deception  during  the  World  War,  but  they 
served  most  prominently  in  the  later  stages  of 
the  war  upon  the  sea.  Inasmuch  as  the  story  of  the 
science  of  camouflage  is  not  generally  available,  it 
appears  worth  while  to  present  it  briefly.  Besides 
being  of  interest,  it  will  reveal  to  the  reader  the  part 
that  the  science  of  light,  color,  lighting,  and  vision 
played  in  deception.  Furthermore,  the  reader  will 
sense  the  numberless  illusions  which  are  woven  into 
camouflage  as  developed  in  nature,  and  in  human 
activities.  The  word  camouflage  by  origin  does  not 
include  all  kinds  of  deception;  however,  by  exten- 
sion it  may  and  will  here  signify  almost  the  entire 
art  and  science  of  deception  as  found  in  nature  and 
as  practiced  in  the  World  War. 

Terrestrial  Camouflage.  —  Camouflage  is  an  art 
which  is  the  natural  outgrowth  of  our  instinct  for  con- 
cealment and  deception  when  pitting  our  wits  against 
those  of  a  crafty  prey  or  enemy.  It  is  an  art  older 
than  the  human  race,  for  its  beginnings  may  be  traced 
back  to  the  obscurity  of  the  early  ages  of  the  evolution 
of  animal  life.  The  name  was  coined  by  the  French  to 
apply  to  a  definite  art  which  developed  during  the  Great 
War  to  a  high  state,  as  many  other  arts  developed 

by  drawing  deeply  upon  the  resources  of  scientific 

210 


CAMOUFLAGE  211 


knowledge.  With  the  introduction  of  this  specific 
word  to  cover  a  vast  field  of  activity  in  scientifically 
concealing  and  deceiving,  many  are  led  to  believe 
that  this  is  a  new  art,  but  such  is  not  the  case.  How- 
ever, like  many  other  arts,  such  as  that  of  flying,  the 
exigencies  of  modern  warfare  have  provided  an  impetus 
which  has  resulted  hi  a  highly  developed  art. 

Scientists  have  recognized  for  many  years,  and 
perhaps  more  or  less  vaguely  for  centuries,  that 
Nature  exhibits  wonderful  examples  of  concealment 
and  deception.  The  survival  of  the  fittest,  as  Darwin 
expressed  his  doctrine,  included  those  individuals 
of  a  species  who  were  best  fitted  by  their  markings 
and  perhaps  by  peculiar  habits  to  survive  hi  the  en- 
vironment in  which  they  lived.  Naturally,  markings, 
habits,  and  environment  became  more  and  more 
adapted  to  each  other  until  the  species  became  in 
equilibrium  with  Nature  sufficiently  to  insure  its  per- 
petuity. If  we  look  about  us  upon  animal  life  we  see 
on  every  hand  examples  of  concealing  coloration  and 
attitudes  designed  to  deceive  the  prey  or  enemy. 
The  rabbit  is  mottled  because  Nature's  infinite  variety 
of  highlights,  shadows,  and  hues  demand  variety  in 
the  markings  of  an  animal  if  the  latter  is  to  be  se- 
curely hidden.  Solid  color  does  not  exist  in  Nature's 
landscapes  in  large  areas.  The  rabbit  is  lighter 
underneath  to  compensate  for  the  lower  intensity  of 
illumination  received  on  these  portions.  As  winter 
approaches,  animals  in  rigorous  climates  need  warmer 
coats,  and  the  hairs  grow  longer.  In  many  cases  the 
color  of  the  hairs  changes  to  gray  or  white,  providing 
a  better  coating  for  the  winter  environment. 


212  VISUAL  ILLUSIONS 

Animals  are  known  to  mimic  inanimate  objects 
for  the  sake  of  safety.  For  example,  the  bittern  will 
stand  rigid  with  its  bill  pointed  skyward  for  many 
minutes  if  it  suspects  an  enemy.  Non-poisonous 
snakes  resemble  poisonous  ones  in  general  charac- 
teristics and  get  along  in  the  world  on  the  reputation 
of  their  harmful  relatives.  The  drone-bee  has  no 
sting,  but  to  the  casual  observer  it  is  a  bee  and  bees 
generally  sting.  Some  animals  have  very  contrasting 
patterns  which  are  conspicuous  in  shape,  yet  these 
very  features  disguise  the  fact  that  they  are  animals. 
Close  observation  of  fishes  in  their  natural  environ- 
ment provides  striking  examples  of  concealing  colora- 
tion. Vast  works  have  been  written  on  this  subject 
by  scientists,  so  it  will  only  be  touched  upon  here. 

There  are  many  examples  of  "  mobile  "  camouflage 
to  be  found  in  Nature.  Seasonal  changes  have  been 
cited  in  a  foregoing  paragraph.  The  chameleon  changes 
its  color  from  moment  to  moment.  The  flounder 
changes  its  color  and  pattern  to  suit  its  environment. 
It  will  even  strive  to  imitate  a  black  and  white  checker- 
board. 

In  looking  at  a  bird,  animal,  insect,  or  other  living 
thing  it  is  necessary  to  place  it  in  its  natural  environ- 
ment at  least  in  the  imagination,  before  analyzing  its 
coloration.  For  example,  a  male  mallard  duck  hanging 
in  the  market  is  a  very  gaudy  object,  but  place  it  in 
the  pond  among  the  weeds,  the  green  leaves,  the 
highlights,  and  the  shadows,  and  it  is  surprisingly 
inconspicuous.  The  zebra  in  the  zoo  appears  to  be 
marked  for  the  purpose  of  heralding  its  presence 
anywhere  in  the  range  of  vision,  but  in  its  reedy,  bushy, 


CAMOUFLAGE  213 


grassy  environment  it  is  sufficiently  inconspicuous 
for  the  species  to  survive  in  Nature's  continuous 
warfare. 

Thus  studies  of  Nature  reveal  the  importance  of 
general  hue,  the  necessity  for  broken  color  or  pattern, 
the  fact  that  black  spots  simulate  shadows  or  voids, 
the  compensation  for  lower  illumination  by  counter- 
shading,  and  many  other  facts.  The  artist  has  aided 
in  the  development  of  camouflage,  but  the  definite 
and  working  basis  of  all  branches  of  camouflage  are 
the  laws  and  facts  of  light,  color,  and  vision  as  the 
scientist  knows  them. 

Just  as  lower  animal  life  has  unconsciously  sur- 
vived or  evolved  by  being  fitted  to  do  so,  mankind 
has  consciously,  or  at  least  instinctively,  applied 
camouflage  of  various  kinds  to  fool  his  prey  or  his 
enemy.  Many  of  us  in  hunting  ducks  have  concealed 
the  bow  of  our  sneak-boat  with  mud  and  weeds,  or  in 
the  season  of  floating  ice,  with  a  white  cloth.  In 
our  quest  of  water  fowl  we  use  decoys  and  grass  suits. 
The  Esquimau  stalks  his  game  behind  a  piece  of  ice. 
In  fact,  on  every  hand  we  find  evidences  of  this  natural 
instinct.  The  Indian,  painted  his  face  and  body  in  a 
variety  of  colors  and  patterns.  Did  he  do  this  merely 
to  be  hideous?  It  seems  very  possible  that  the  same 
instinct  which  made  him  the  supreme  master  of  wood- 
craft caused  him  to  reap  some  of  the  advantages  of 
concealment  due  to  the  painting  of  his  face  and  body. 

In  past  wars  there  is  plenty  of  evidence  that  con- 
cealment and  deception  were  practiced  to  the  full 
extent  justifiable  by  the  advantages  or  necessity.  In 
the  World  War  the  advent  of  the  airplane  placed  the 


214  VISUAL  ILLUSIONS 

• 
third  dimension  in  reconnaissance  and  called  for  the 

application  of  science  in  the  greatly  extended  necessity 
for  concealment  and  deception.  With  the  advent  of 
the  airplane,  aerial  photography  became  a  more  im- 
portant factor  than  visual  observation  in  much  of  the 
reconnaissance.  This  necessitated  that  camouflage 
in  order  to  be  successful  had  to  meet  the  requirements 
of  the  photographic  eye,  as  well  as  that  of  the  human 
eye.  In  other  words,  the  special  characteristics  of  the 
colors  used  had  to  be  similar  to  those  of  Nature's 
colors.  For  example,  chlorophyl,  the  green  coloring 
matter  of  vegetation,  is  a  peculiar  green  as  compared 
with  green  pigments.  When  examined  with  a  spectro- 
scope it  is  seen  to  reflect  a  band  of  deep  red  light  not 
reflected  by  ordinary  pigments.  In  considering  this 
aspect  it  is  well  to  bear  in  mind  that  the  eye  is  a  syn- 
thetic apparatus;  that  is  does  not  analyze  color  in  a 
spectral  sense.  An  artist  who  views  color  subjectively 
and  is  rarely  familiar  with  the  spectral  basis  may 
match  a  green  leaf  perfectly  with  a  mixture  of  pig- 
ments. A  photographic  plate,  a  visual  filter,  or  a 
spectroscope  will  reveal  a  difference  which  the  un- 
aided eye  does  not. 

Some  time  before  the  Great  War  began,  it  oc- 
curred to  the  writer  that  colored  filters  could  be 
utilized  in  aiding  vision  by  increasing  the  contrast 
of  the  object  to  be  viewed  against  its  surroundings.9 
Studies  were  made  of  various  filters,  made  with  the 
object  of  the  experiment  in  mind,  in  viewing  the  uni- 
forms of  various  armies.  Further  developments  were 
made  by  applying  the  same  principles  to  colored  lights 
and  painted  pictures.  Many  of  these  have  been 


CAMOUFLAGE  215 


described  elsewhere.  With  the  development  of  the 
science  of  camouflage,  filters  came  into  use  for  the 
detection  of  camouflage.  As  a  result  of  the  demand 
for  avoiding  detection  by  photographic  plates  and  by 
various  colored  filters,  some  paints  provided  for  the 
camoufleur  were  developed  according  to  the  spectral 
requirements.  Many  other  applications  of  science 
were  developed  so  that  camouflage  can  now  be  called 
an  art  based  upon  sound  scientific  principles. 

Natural  lighting  is  so  variable  that  it  is  often 
impossible  to  provide  camouflage  which  will  remain 
satisfactory  from  day  to  day;  therefore,  a  broad]  knowl- 
edge of  Nature's  lighting  is  necessary  in  order  to 
provide  the  best  compromise.  There  are  two  sources 
of  light  in  the  daytime,  namely,  the  sun  and  the  sky. 
The  relative  amounts  of  light  contributed  by  these 
two  sources  is  continually  changing.  The  sky  on 
cloudless  days  contributes  from  one-tenth  to  one- 
third  of  the  total  light  received  by  a  horizontal  surface 
at  noon.  Light  from  the  sky  and  light  reflected  from 
the  surroundings  illuminate  the  shadows.  These 
shadows  are  different  in  color  than  highlights,  al- 
though these  finer  distinctions  may  be  ignored  in 
most  camouflage  because  color  becomes  less  con- 
spicuous as  the  distance  of  observation  increases.  In 
general,  the  distribution  of  brightness  or  light 
and  shade  is  the  most  important  aspect  to  be  con- 
sidered. 

The  camoufleur  worries  over  shadows  more  than 
any  other  aspect  generally.  On  overcast  days  camou- 
flage is  generally  much  more  successful  than  on  sunny 
days.  Obviously,  counter-shading  is  resorted  to  in 


216  VISUAL  ILLUSIONS 

order  to  eliminate  shadows,  and  where  this  is  unsuc- 
cessful confusion  is  resorted  to  by  making  more 
shadows.  The  shape  and  orientation  of  a  building  is 
very  important  to  those  charged  with  the  problem  of 
rendering  it  inconspicuous  to  the  enemy,  but  little 
attention  has  been  paid  to  these  aspects.  For  ex- 
ample, a  hangar  painted  a  very  satisfactory  dull  green 
will  be  distinguishable  by  its  shape  as  indicated  by 
its  shadow  and  shaded  sides.  In  this  zone  a  hangar, 
for  example,  would  be  more  readily  concealed  if  its 
length  lay  north  and  south.  Its  sides  could  be  brought 
with  a  gradual  curve  to  the  ground  and  its  rear,  which 
is  during  most  of  the  day  in  shadow,  could  be  effectively 
treated  to  conceal  the  shadow.  A  little  thought  will 
convince  the  reader  of  the  importance  of  shape  and 
orientation. 

Broken  color  or  pattern  is  another  fundamental 
of  camouflage  which,  of  course,  must  be  adapted  to 
its  environment.  For  our  trucks,  cannon,  and  many 
other  implements  of  war,  dark  green,  yellow,  dark 
blue,  light  gray,  and  other  colors  have  been  used  in 
a  jumble  of  large  patterns.  A  final  refinement  is  that 
of  the  blending  of  these  colors  at  a  distance,  where 
the  eye  no  longer  resolves  the  individual  patches, 
to  a  color  which  simulates  the  general  hue  of  the  sur- 
roundings. For  example,  red  and  green  patches  at 
a  distance  blend  to  yellow;  yellow  and  blue  patches 
blend  to  a  neutral  gray  if  suitably  balanced,  but  if  not, 
to  a  yellow-gray  or  a  blue-gray;  red,  green,  and  blue 
if  properly  balanced  will  blend  to  a  gray;  black, 
white  and  green  patches  will  blend  to  a  green  shade, 
and  so  on.  These  facts  are  simple  to  those  who  are 


CAMOUFLAGE  217 


familiar  with  the  science  of  light  and  color,  but  the 
artist,  whose  knowledge  is  based  upon  the  mixture 
of  pigments,  sometimes  errs  in  considering  this  aspect 
of  color-blending  by  distance.  For  example,  it  is  not 
uncommon  for  him  to  state  that  at  a  distance  yellow 
and  blue  patches  blend  to  make  green,  but  the  addi- 
tion of  lights  or  of  juxtaposed  colors  is  quite  different 
in  result  from  the  addition  of  pigments  by  intimately 
mixing  them. 

In  constructing  such  a  pattern  of  various  colors  it 
is  also  desirable  to  have  the  final  mean  brightness 
approximate  that  of  the  general  surroundings.  This 
problem  can  be  solved  by  means  of  the  photometer 
and  a  formula  provided,  which  states,  for  example, 
that  a  certain  percentage  of  the  total  area  be  painted 
in  gray,  another  percentage  in  green,  and  so  on.  The 
photometer  has  played  an  important  role  in  establish- 
ing the  scientific  basis  of  camouflage.  The  size  of  the 
pattern  must  be  governed  by  the  distance  at  which 
it  is  to  be  viewed,  for  obviously  if  too  small  the  effect 
is  that  of  solid  color,  and  if  too  large  it  will  render  the 
object  conspicuous,  which  is  a  disadvantage  ranking 
next  to  recognizable. 

Where  the  artist  is  concerned  with  a  background 
which  does  not  include  the  sky,  that  is,  where  he 
deals  only  with  illuminated  objects  on  the  earth, 
his  trained  eye  is  valuable  provided  the  colors  used 
meet  the  demands  made  by  photographic  plates  and 
visual  color-filters.  In  other  words,  the  sky  as  a  back- 
ground gives  trouble  to  all  who  are  unfamiliar  with 
scientific  measurements.  The  brightnesses  of  sky 
and  clouds  are  outside  the  scale  of  brightnesses  ordi- 


218  VISUAL  ILLUSIONS 

narily  encountered  in  a  landscape.  Many  interesting 
instances  of  the  artist's  mistakes  in  dealing  with  these 
backgrounds  could  be  presented ;  however,  the  artist's 
trained  eye  has  been  a  great  aid  in  constructing 
patterns  and  various  other  types  of  camouflage. 
One  of  the  most  conspicuous  aspects  of  the  earth's 
surface  is  its  texture.  From  great  heights  it  appears 
flat,  that  is,  rolling  land  is  ironed  out  and  the  general 
contour  of  the  ground  is  flattened.  However,  the 
element  of  texture  always  remains.  This  is  the  chief 
reason  for  the  extensive  use  of  netting  on  which  dyed 
raffia,  foliage,  pieces  of  colored  cloth,  etc.,  are  tied. 
Such  network  has  concealed  many  guns,  headquarters, 
ammunition  dumps,  communication  trenches,  road- 
ways, etc.  When  this  has  been  well  done  the  con- 
cealment is  perfect. 

One  of  the  greatest  annoyances  to  the  camoufleur 
is  the  lack  of  dullness  or  "  flatness  "  of  the  paints, 
fabrics,  and  some  of  the  other  media  used.  When 
viewed  at  some  angles  the  glint  of  highlights  due  to 
specular  reflection  renders  the  work  very  conspicu- 
ous. For  this  reason  natural  foliage  or  such  material 
as  dyed  raffia  has  been  very  successful. 

Systems  of  network  and  vertical  screens  have 
been  extensively  employed  on  roadways  near  the 
front,  not  for  the  purpose  of  concealing  from  the  enemy 
the  fact  that  the  roadways  exist,  but  to  make  it  neces- 
sary to  shell  the  entire  roadway  continually  if  it  is 
hoped  to  prevent  its  use. 

Although  the  camoufleur  is  provided  with  a  vast 
amount  of  material  for  his  work,  many  of  his  require- 
ments are  met  by  the  material  at  hand.  Obviously, 


CAMOUFLAGE  219 


the  most  convenient  method  of  providing  concealment 
for  a  given  environment  is  to  use  the  materials  of  the 
environment.  Hence,  rubbish  from  ruined  buildings 
or  villages  supplies  camouflage  for  guns,  huts,  etc.,  in 
that  environment.  In  woods  the  material  to  simulate 
the  woods  is  at  hand.  Many  of  these  aspects  are  so 
obvious  to  the  reader  that  space  will  not  be  given  to 
their  consideration.  The  color  of  the  soil  is  important, 
for  if  it  is  conspicuous  the  camoufleur  must  provide 
screens  of  natural  turf. 

In  this  great  game  of  hocus-pocus  many  deceptions 
are  resorted  to.  Replicas  of  large  guns  and  trenches 
are  made ;  dummy  soldiers  are  used  to  foil  the  sniper 
and  to  make  him  reveal  his  location,  and  papier-mache 
horses,  trees,  and  other  objects  conceal  snipers  and 
observers  and  afford  listening  posts.  Gunners  have 
been  dressed  in  summer  in  green  flowing  robes.  In 
winter  white  robes  have  been  utilized.  How  far  away 
from  modern  warriors  are  all  the  usual  glitter  and 
glamour  of  military  impedimenta  in  the  past  parades 
of  peace  time!  The  armies  now  dig  in  for  conceal- 
ment. The  artillery  is  no  longer  invisible  behind 
yonder  hill,  for  the  eyes  of  the  aerial  observer  of  the 
camera  reveal  its  position  unless  camouflaged  for 
the  third  dimension. 

In  the  foregoing  only  the  highlights  of  a  vast  art 
have  been  viewed,  but  the  art  is  still  vaster,  for  it 
extends  into  other  fields.  Sound  must  sometimes  be 
camouflaged  and  this  can  only  be  done  by  using  the 
same  medium  —  sound.  In  these  days  of  scientific 
warfare  it  is  to  be  expected  that  the  positions  of  enemy 
guns  would  be  detected  by  other  means  than  em- 


220  VISUAL  ILLUSIONS 

ployed  in  the  past.  A  notable  method  is  the  use  of 
velocity  of  sound.  Records  are  made  at  various 
stations  of  the  firing  of  a  gun  and  the  explosion  of  the 
shell.  By  trigonometric  laws  the  position  of  the  gun 
is  ascertained.  It  is  said  that  the  Germans  fired  a 
number  of  guns  simultaneously  with  the  "  75-mile  " 
gun  in  order  to  camouflage  its  location.  The  airplane 
and  submarine  would  gladly  employ  sound  camou- 
flage in  order  to  foil  the  sound  detector  if  practicable 
solutions  were  proposed. 

The  foregoing  is  a  brief  statement  of  some  of  the 
fundamental  principles  of  land  camouflage.  Let  us 
now  briefly  consider  the  eyes  of  the  enemy.  Of 
course,  much  concealment  and  deception  is  devised 
to  foil  the  observer  who  is  on  the  ground  and  fairly 
close.  The  procedure  is  obvious  to  the  average 
imagination;  however,  the  reader  may  not  be  ac- 
quainted with  the  aerial  eyes  from  which  conceal- 
ment is  very  important.  As  one  ascends  in  an  air- 
plane to  view  a  landscape  he  is  impressed  with  the 
inadequacy  of  the  eyes  to  observe  the  vast  number 
of  details  and  of  the  mind  to  retain  them.  Field 
glasses  cannot  be  used  as  satisfactorily  in  an  air- 
plane as  on  solid  ground,  owing  to  vibration  and  other 
movements.  The  difference  is  not  as  great  in  the 
huge  flying  boats  as  it  is  in  the  ordinary  airplane. 
The  camera  can  record  many  details  with  higher 
accuracy  than  the  eye.  At  an  altitude  of  one  mile 
the  lens  can  be  used  at  full  aperture  and  thus  very 
short  exposures  are  possible.  This  tends  to  avoid  the 
difficulty  due  to  vibration.  When  the  plates  are  de- 
veloped for  detail  and  enlargements  are  made,  many 


CAMOUFLAGE  221 


minute  details  are  distinguishable.  Furthermore,  ow- 
ing to  the  fact  that  the  spectral  sensibilities  of  pho- 
tographic emulsions  differ  from  that  of  the  eye,  con- 
trasts are  brought  out  which  the  eye  would  not  see. 
This  applies  also  to  camouflage  which  is  devised 
merely  to  suit  the  eye.  Individual  footprints  have 
been  distinguished  on  prints  made  from  negatives 
exposed  at  an  altitude  of  6000  feet.  By  means  of 
photography,  daily  records  can  be  made  if  desired 
and  these  can  be  compared.  A  slight  change  is  readily 
noted  by  such  comparison  by  skilled  interpreters  of 
aerial  photographs.  The  disappearance  of  a  tree  from 
a  clump  of  trees  may  arouse  suspicion.  Sometimes 
a  wilted  tree  has  been  noted  on  a  photograph  which 
naturally  attracts  attention  to  this  position.  It  has 
been  said  that  the  belligerents  resorted  to  trans- 
planting trees  a  short  distance  at  a  time  from  day 
to  day  in  order  to  provide  clearance  for  newly  placed 
guns.  By  paths  converging  toward  a  certain  point, 
it  may  be  concluded  from  the  photographs  that  an 
ammunition  dump  or  headquarters  is  located  there 
even  though  the  position  itself  was  well  camouflaged. 
Continuous  photographic  records  may  reveal  dis- 
turbances of  turf  and  lead  to  a  more  careful  inspection 
of  the  region  for  sapping  operations,  etc.  By  these 
few  details  it  is  obvious  that  the  airplane  is  responsible 
for  much  of  the  development  of  camouflage  on  land, 
owing  to  the  necessity  which  it  created  for  a  much 
more  extensive  concealment.  The  entire  story  of 
land  camouflage  would  overflow  the  confines  of  a 
volume,  but  it  is  hoped  that  the  foregoing  will  aid 
the  reader  in  visualizing  the  magnitude  of  the  art  and 


222  VISUAL  ILLUSIONS 

the  scientific  basis  upon  which  terrestial  camouflage 
is  founded. 

Marine  Camouflage.  — At  the  time  of  the  Spanish- 
American  war,  our  battleships  were  painted  white, 
apparently  with  little  thought  of  attaining  low  visi- 
bility. Later  the  so-called  "  battleship  gray "  was 
adopted,  but  it  has  been  apparent  to  close  observers 
that  this  gray  is  in  general  too  dark.  Apparently  it 
is  a  mixture  of  black  and  white.  The  ships  of  the 
British  navy  were  at  one  time  painted  black,  but 
preceding  the  Great  War  their  coats  were  of  a  warm 
dark  gray.  Germany  adopted  dark  gray  before  the 
close  of  the  last  century  and  Austria  adopted  the 
German  gray  at  the  outbreak  of  the  war.  The  French 
and  Italian  fleets  were  also  painted  a  warm  gray. 
This  development  toward  gray  was  the  result  of  an 
aim  toward  attaining  low  visibility.  Other  changes 
were  necessitated  by  submarine  warfare  which  will 
be  discussed  later. 

In  the  early  days  of  unrestricted  submarine  war- 
fare many  schemes  for  modifying  the  appearance 
of  vessels  were  submitted.  Many  of  these  were 
merely  wild  fancies  with  no  established  reasoning 
behind  them.  Here  again  science  came  to  the  rescue 
and  through  research  and  consultation,  finally  straight- 
ened out  matters.  The  question  of  low  visibility  for 
vessels  could  be  thoroughly  studied  on  a  laboratory 
scale,  because  the  seascape  and  natural  lighting  con- 
ditions could  be  reproduced  very  closely.  Even  the 
general  weather  conditions  could  be  simulated,  al- 
though, of  course,  the  experiments  could  be  prose- 
cuted outdoors  with  small  models,  as  indeed  they 


CAMOUFLAGE  223 


were.  Mr.  L.  A.  Jones  10  carried  out  an  investiga- 
tion on  the  shore  of  Lake  Ontario,  and  laboratory 
experiments  were  conducted  by  others  with  the 
result  that  much  light  was  shed  on  the  questions  of 
marine  camouflage.  This  work  confirmed  the  con- 
clusion of  the  author  and  others  that  our  battleship 
gray  was  too  dark.  Of  course,  the  color  best  adapted 
is  that  which  is  the  best  compromise  for  the  extreme 
variety  in  lighting  and  weather  conditions.  These 
vary  in  different  parts  of  the  world,  so  naturally  those 
in  the  war  zone  were  of  primary  importance.  All 
camouflage  generally  must  aim  to  be  a  compromise 
best  suited  for  average  or  dominating  conditions. 
For  example,  in  foggy  weather  a  certain  paint  may 
render  a  ship  of  low  visibility,  but  on  a  sunny  day  the 
ship  might  be  plainly  visible.  However,  if  ships  are 
rendered  of  low  visibility  for  even  a  portion  of  the 
time  it  is  obvious  that  an  advantage  has  been  gained. 
Cloudiness  increases  generally  from  the  equator 
northward,  as  indicated  by  meteorological  annals. 

In  order  to  study  low  visibility  a  scale  of  visibility 
must  be  established,  and  it  is  essential  to  begin  with 
the  fundamentals  of  vision.  We  distinguish  objects 
by  contrasts  in  brightness  and  in  color  and  we  recog- 
nize objects  by  these  contrasts  which  mold  their 
forms.  In  researches  in  vision  it  is  customary  to  devise 
methods  by  which  these  contrasts  can  be  varied.  This 
is  done  by  increasing  or  decreasing  a  veil  of  luminosity 
over  the  object  and  its  surroundings  and  by  other 
means.  Much  work  has  been  done  in  past  years  hi 
studying  the  minimum  perceptible  contrast,  and  it 
has  been  found  to  vary  with  hue,  with  the  magnitude 


224  VISUAL  ILLUSIONS 

of  brightness,  and  with  the  size  of  the  image,  that  is, 
with  the  distance  of  an  object  of  given  size.  In  such 
problems  as  this  one  much  scientific  work  can  be 
drawn  upon.  A  simple,  though  rough,  scale  of  visi- 
bility may  be  made  by  using  a  series  of  photographic 
screens  of  different  densities.  A  photographic  screen 
is  slightly  diffusing,  still  the  object  can  be  viewed 
through  it  very  well.  Such  methods  have  been 
employed  by  various  investigators  in  the  study  of 
visibility. 

Owing  to  the  curvature  of  the  earth,  the  distance 
at  which  a  vessel  can  be  seen  on  a  clear  day  is  limited 
by  the  height  of  the  observer  and  of  the  ship's  super- 
structure. For  an  observer  in  a  certain  position  the 
visibility  range  varies  as  the  square  root  of  the  distance 
of  the  object  from  him.  Such  data  are  easily  avail- 
able, so  they  will  not  be  given  here.  So  far  we  have 
considered  the  ship  itself  when,  as  a  matter  of  fact, 
on  clear  days  the  smoke  cloud  emitted  by  the  ship 
is  usually  visible  long  before  a  ship's  superstructure 
appears  on  the  horizon.  This  led  to  the  prevention 
of  smoke  by  better  combustion,  by  using  smoke- 
less fuels,  etc. 

The  irregular  skyline  of  a  ship  is  perhaps  one  of 
the  most  influential  factors  which  tend  to  increase 
its  visibility.  Many  suggestions  pertaining  to  the 
modification  of  the  superstructure  have  been  made, 
but  these  are  generally  impracticable.  False  work 
suffers  in  heavy  seas  and  high  winds. 

After  adopting  a  suitable  gray  as  a  "low-visi- 
bility "  paint  for  ships,  perhaps  the  next  refinement 
was  counter  shading;  that  is,  shadows  were  painted 


CAMOUFLAGE  225 


a  lighter  color,  or  even  white.  The  superstructure 
was  painted  in  some  cases  a  light  blue,  with  the  hope 
that  it  would  fade  into  the  distant  horizon.  How- 
ever, the  effectiveness  of  the  submarine  demanded 
new  expedients  because  within  its  range  of  effective- 
ness no  ingenuity  could  render  its  intended  prey 
invisible.  The  effective  gun-fire  from  submarines  is 
several  miles  and  torpedoes  can  be  effective  at  these 
distances.  However,  the  submarine  prefers  to  dis- 
charge the  torpedo  at  ranges  within  a  mile.  It  is 
obvious  that,  in  average  weather,  low  visibility  ceases 
to  be  very  effective  against  the  submarine.  The 
movement  of  a  target  is  of  much  less  importance  in 
the  case  of  gun-fire  than  in  the  case  of  the  torpedo 
with  its  relatively  low  velocity.  The  submarine 
gunner  must  have  the  range,  speed,  and  course  of 
the  target  in  order  to  fire  a  torpedo  with  any  hope  of 
a  hit.  Therefore,  any  uncertainties  that  could  be 
introduced  pertaining  to  these  factors  would  be  to 
the  advantage  of  the  submarine's  prey.  For  ex- 
ample, low  visibility  gave  way  to  confusibility  in  the 
discussions  of  defence  against  the  submarine  and 
the  slogan,  "  A  miss  is  as  good  as  a  mile  "  was  adopted. 
The  foregoing  factors  cannot  be  determined  ordinarily 
with  high  accuracy,  so  that  it  appeared  possible  to  add 
somewhat  to  the  difficulties  of  the  submarine  com- 
mander. 

Many  optical  illusions  have  been  devised  and 
studied  by  scientists.  In  fact,  some  of  these  tricks 
are  well  known  to  the  general  reader.  Straight  lines 
may  appear  broken,  convergent,  or  divergent  by  pro- 
viding certain  patterns  or  lines  intermingled  with 


226 


VISUAL  ILLUSIONS 


them.  Many  of  these  were  applied  to  models  in 
laboratory  experiments  and  it  has  been  shown  that 
confusion  results  as  to  the  course  of  the  vessel.  The 
application  of  these  on  vessels  has  resulted  in  the 
grotesque  patterns  to  be  seen  on  ships  during  the 
latter  stage  of  the  war.  It  is  well  known  that  these 
illusions  are  most  effective  when  the  greatest  con- 
trasts are  used,  hence  black  and  white  patterns  are 
common.  Color  has  not  been  utilized  as  definitely 


Fig.  92.  —  A  primary  stage  in  the  evolution  of  the  use  of  geometrical- 
optical  illusions  on  ships. 

as  pattern  in  confusibility,  although  there  is  a  sec- 
ondary aim  of  obtaining  low  visibility  at  a  great  distance 
by  properly  balancing  the  black,  white,  and  other 
colors  so  that  a  blue-gray  results  at  distances  too 
great  for  the  individual  patterns  to  be  resolved  by  the 
eye.  Color  could  be  used  for  the  purpose  of  increasing 
the  conclusion  by  apparently  altering  the  perspective. 
For  example,  blue  and  red  patterns  on  the  same 
surface  do  not  usually  appear  at  the  same  distance, 
the  red  appearing  closer  than  the  blue. 

Such  apparently  grotesque  patterns  aimed  to  dis- 
tort the  lines  of  the  ship  and  to  warp  the  perspective 


CAMOUFLAGE  227 


by  which  the  course  is  estimated.  This  was  the  final 
type  of  marine  camouflage  at  the  close  of  the  war. 
Besides  relying  upon  these  illusions,  ships  zigzagged 
on  being  attacked  and  aimed  in  other  ways  to  con- 
fuse the  enemy.  No  general  attempt  was  made  to 
disguise  the  bow,  because  the  bow-wave  was  gen- 
erally visible.  However,  attempts  have  been  made 
to  increase  it  apparently  and  even  to  provide  one  at 
the  stern.  In  fact,  ingenuity  was  heavily  drawn  upon 
and  many  expedients  were  tried. 

After  low-visibility  was  abandoned  in  favor  of 
the  optical  illusion  for  frustrating  the  torpedo-attack 
by  the  submarine,  there  was  a  period  during  which 
merely  a  mottled  pattern  was  used  for  vessels.  Gradu- 
ally this  evolved  toward  such  patterns  as  shown  in 
Fig.  92.  In  this  illustration  it  is  seen  that  the  optical- 
illusion  idea  has  taken  definite  form.  During  the 
period  of  uncertainty  as  to  the  course  the  pattern 
should  take,  a  regularity  of  pattern  was  tried,  such 
as  illustrated  in  Figs.  93  and  94.  Finally,  when  it 
dawned  more  or  less  simultaneously  upon  various 
scientific  men,  who  were  studying  the  problems  of 
protecting  vessels  upon  the  seas,  that  the  geometrical- 
optical  illusion  in  its  well-known  forms  was  directly 
adaptable,  renewed  impetus  was  given  to  investiga- 
tion. The  scientific  literature  yielded  many  facts 
but  the  problems  were  also  studied  directly  by  means 
of  models.  The  latter  study  is  illustrated  by  Figs. 
95  and  96,  the  originals  having  been  furnished  by 
Mr.  E.  L.  Warner,11  who  among  others  prosecuted  a 
study  of  the  application  of  illusions  to  vessels.  The 
final  results  were  gratifying,  as  shown  to  some  extent 


228 


VISUAL  ILLUSIONS 


Figs.  93  and  94. —  Attempts  at  distortion  of  outline  which  preceded  the 
adoption  of  geometrical-optical  illusions  for  ships. 


CAMOUFLAGE 


229 


Figs.  95  and  96.    Illustrating  the  use  of   models  by  the  Navy  Depart- 
ment in  developing  the  geometrical-illusion  for  ships. 


230  VISUAL  ILLUSIONS 

in  Figs.  97  and  98,  also  kindly  furnished  by  Mr.  Warner. 
It  is  seen  that  these  patterns  are  really  deceiving  as 
to  the  course  of  the  vessel. 

The  convoy  system  is  well  known  to  the  reader. 
This  saved  many  vessels  from  destruction.  Vessels 
of  the  same  speed  were  grouped  together  and  steamed 
in  flocks  across  the  Atlantic.  Anyone  who  has  Lad 
the  extreme  pleasure  of  looking  down  from  an  air- 
plane upon  these  convoys  led  by  destroyers  and  at- 
tended by  chasers  is  strongly  impressed  with  the 
old  adage,  "  In  unity  there  is  strength." 

Before  the  war  began,  a  Brazilian  battleship 
launched  in  this  country  was  provided  with  a  system 
of  blue  lights  for  use  when  near  the  enemy  at  night. 
Blue  was  adopted  doubtless  for  its  low  range  com- 
pared with  light  of  other  colors.  We  know  that  the 
setting  sun  is  red  because  the  atmospheric  dust, 
smoke,  and  moisture  have  scattered  and  absorbed 
the  blue  and  green  rays  more  than  the  red  and  yellow 
rays.  In  other  words  the  penetrating  power  of  the 
red  and  yellow  is  greater  than  that  of  the  blue  rays. 
This  country  made  use  of  this  expedient  to  some 
extent.  Of  course,  all  other  lights  were  extinguished 
and  portholes  were  closed  in  ocean  travel  during  the 
submarine  menace. 

Naturally  smoke-screens  were  adopted  as  a  de- 
fensive measure  on  sea  as  well  as  on  land.  Destroyers 
belch  dense  smoke  from  their  stacks  in  order  to  screen 
battleships.  Many  types  of  smoke-boxes  have  been 
devised  or  suggested.  The  smoke  from  these  is 
produced  chemically  and  the  apparatus  must  be 
simple  and  safe.  If  a  merchantman  were  attacked 


CAMOUFLAGE 


231 


97  and  98.  —  Examples  of  the  geometrical-optical  illusion  as 
finally  applied. 


232  VISUAL  ILLUSIONS 

\ 


by  a  submarine  immediately  smoke-boxes  would  be 
dumped  overboard  or  some  which  were  installed  on 
deck  would  be  put  into  operation  and  the  ship  would 
be  steered  in  a  zigzag  course.  These  expedients  were 
likely  to  render  shell-fire  and  observations  inac- 
curate. This  mode  of  defense  is  obviously  best 
suited  to  unarmed  vessels.  In  the  use  of  smoke- 
boxes  the  direction  and  velocity  of  the  wind  must  be 
considered.  The  writer  is  unacquainted  with  any 
attempts  made  to  camouflage  submarines  under  water, 
but  that  this  can  be  done  is  evident  from  aerial  ob- 
servations. When  looking  over  the  water  from  a 
point  not  far  above  it,  as  on  a  pier,  we  are  unable  to  see 
into  the  water  except  at  points  near  us  where  our 
direction  of  vision  is  not  very  oblique  to  the  surface 
of  the  water.  The  brightness  of  the  surface  of  water 
is  due  to  mirrored  sky  and  clouds  ordinarily.  For  a 
perfectly  smooth  surface  of  water,  the  reflection 
factor  is  2  per  cent  for  perpendicular  incidence.  This 
increases  only  slightly  as  the  obliquity  increases  to  an 
angle  of  about  60  degrees.  From  this  point  the  re- 
flection-factor of  the  surface  rapidly  increases,  be- 
coming 100  per  cent  at  90  degrees  incidence.  This 
accounts  for  the  ease  with  which  we  can  see  into  the 
water  from  a  position  directly  overhead  and  hence 
the  airplane  has  been  an  effective  hunter  of  sub- 
merged submarines.  The  depth  at  which  an  object 
can  be  seen  in  water  depends,  of  course,  upon  its 
clarity.  It  may  be  surprising  to  many  to  learn  that 
the  brightness  of  water,  such  as  rivers,  bays,  and 
oceans,  as  viewed  perpendicularly  to  its  surface,  is 
largely  due  to  light  diffused  within  it.  This  point 


CAMOUFLAGE  233 


became  strikingly  evident  during  the  progress  of  work 
in  aerial  photometry. 

A  submerged  submarine  may  be  invisible  for  two 
reasons:  (1)  It  may  be  deep  enough  to  be  effectively 
veiled  by  the  luminosity  of  the  mass  of  water  above 
it  (including  the  surface  brightness)  or,  (2)  It  may 
be  of  the  proper  brightness  and  color  to  simulate  the 
brightness  and  color  of  the  water.  It  is  obvious  that 
if  it  were  white  it  would  have  to  attain  concealment 
by  submerging  deeply.  If  it  were  a  fairly  dark  green- 
ish-blue it  would  be  invisible  at  very  small  depths. 
In  fact,  it  would  be  of  very  low  visibility  just  below 
the  surface  of  the  water.  By  the  use  of  the  writer's 
data  on  hues  and  reflection-factors  of  earth  and  water 
areas  it  would  be  easy  to  camouflage  submarines 
effectively  from  enemies  overhead.  The  visibility 
of  submarines  is  well  exemplified  by  viewing  large 
fish  such  as  sharks  from  airships  at  low  altitudes. 
They  appear  as  miniature  submarines  dark  gray  or 
almost  black  amid  greenish-blue  surroundings.  In- 
cidentally, the  color  of  water  varies  considerably  from 
the  dirty  yellowish-green  of  shallow  inland  waters 
containing  much  suspended  matter  to  the  greenish- 
blue  of  deep  clear  ocean  waters.  The  latter  as  viewed 
vertically  are  about  one-half  the  brightness  of  the 
former  under  the  same  conditions  and  are  decidedly 
bluer. 

The  Visibility  of  Airplanes.  —  In  the  Great  War 
the  airplane  made  its  debut  in  warfare  and  in  a  short 
time  made  a  wonderful  record,  yet  when  hostilities 
ceased  aerial  camouflage  had  not  been  put  on  a  sci- 
entific basis.  No  nation  had  developed  this  general 


234  VISUAL  ILLUSIONS 

aspect  of  camouflage  systematically  or  to  an  extent 
comparable  with  the  developments  on  land  and  sea. 
One  of  the  chief  difficulties  was  that  scientific  data 
which  were  applicable  were  lacking.  During  the 
author's  activities  as  Chairman  of  the  Committee  on 
Camouflage  of  the  National  Research  Council  he 
completed  an  extensive  investigation  12  of  the  funda- 
mentals upon  which  the  attainment  of  low  visibility 
for  airplanes  must  be  based.  Solutions  of  the  prob- 
lems encountered  in  rendering  airplanes  of  low  visi- 
bility resulted  and  various  recommendations  were 
made,  but  the  experiences  and  data  will  be  drawn 
upon  here  only  in  a  general  way.  In  this  general  re- 
view details  would  consume  too  much  space,  for  the 
intention  has  been  to  present  a  broad  view  of  the 
subject  of  camouflage. 

The  visibility  of  airplanes  presents  some  of  the 
most  interesting  problems  to  be  found  in  the  develop- 
ment of  the  scientific  basis  for  camouflage.  The  gen- 
eral problem  may  be  subdivided  according  to  the  type 
of  airplane,  its  field  of  operation,  and  its  activity. 
For  example,  patrol  craft  which  fly  low  over  our  own 
lines  would  primarily  be  camouflaged  for  low  visibility 
as  viewed  by  enemies  above.  (See  Fig.  99.)  High- 
flying craft  would  be  rendered  of  low  visibility  as 
viewed  primarily  by  the  enemy  below.  Airplanes 
for  night  use  present  other  problems  and  the  visibility 
of  seaplanes  is  a  distinct  problem,  owing  to  the  fact 
that  the  important  background  is  the  water,  because 
seaplanes  are  not  ordinarily  high-flying  craft.  In 
all  these  considerations  it  will  be  noted  that  the 
activity  of  the  airplanes  is  of  primary  importance, 


CAMOUFLAGE 


235 


because  it  determines  the  lines  of  procedure  in  ren- 
dering the  craft  of  low  visibility.  This  aspect  is  too 
complicated  to  discuss  thoroughly  in  a  brief  resume. 

The  same  fundamentals  of  light,  color,  and  vision 
apply  in  this  field  as  in  other  fields  of  camouflage, 


Fig.  99.  —  Representative  earth  backgrounds  for  an  airplane 
(uncamouflaged)  as  viewed  from  above. 


but  different  data  are  required.  When  viewing  air- 
craft from  above,  the  earth  is  the  background  of  most 
importance.  Cumulus  clouds  on  sunny  days  are 
generally  at  altitudes  of  4000  to  7000  feet.  Clouds 
are  not  always  present  and  besides  they  are  of  such 
a  different  order  of  brightness  from  that  of  the  earth 
that  they  cannot  be  considered  in  camouflage  designed 


236  VISUAL  ILLUSIONS 

for  low  visibility  from  above.  In  other  words,  the 
compromise  in  this  case  is  to  accept  the  earth  as  a 
background  and  to  work  on  this  basis.  We  are  con- 
fronted with  seasonal  changes  of  landscape,  but  inas- 
much as  the  summer  landscape  was  of  greatest  im- 
portance generally,  it  was  the  dominating  factor  in 
considering  low  visibility  from  above. 

On  looking  down  upon  the  earth  one  is  impressed 
with  the  definite  types  of  areas  such  as  cultivated 
fields,  woods,  barren  ground  and  water.  Different 
landscapes  contain  these  areas  in  various  propor- 
tions, which  fact  must  be  considered.  Many  thousand 
determinations  of  reflection-factor  and  of  approximate 
hue  were  made  for  these  types  of  areas,  and  upon 
the  mean  values  camouflage  for  low  visibility  as 
viewed  from  above  was  developed.  A  few  values  are 
given  hi  the  accompanying  table,  but  a  more  com- 
prehensive presentation  will  be  found  elsewhere.12 

Mean  Reflection-Factors 

(From  thousands  of  measurements  made  by  viewing  vertically  down- 
ward during  summer  and  fall  from  various  altitudes.) 

Per  Cent 

Woods 4.3 

Barren  ground . . 13.0 

Fields  (grazing  land  and  growing  crops) 6.8 

Inland  water  (rivers  and  bays) 6.8 

Deep  ocean  water 3.5 

Dense  clouds 78.0 

Wooded  areas  are  the  darkest  general  areas  in  a 
landscape  and  possess  a  very  low  reflection-factor. 
From  above  one  sees  the  deep  shadows  interspersed 
among  the  highlights.  These  shadows  and  the  trap- 


CAMOUFLAGE  237 


ping  of  light  are  largely  responsible  for  the  low  bright- 
ness or  apparent  reflection-factor.  This  is  best  il- 
lustrated by  means  of  black  velvet.  If  a  piece  of 
cardboard  is  dyed  with  the  same  black  dye  as  that 
used  to  dye  the  velvet,  it  will  diffusely  reflect  2  or  3 
per  cent  of  the  incident  light,  but  the  black  velvet 
will  reflect  no  more  than  0.5  per  cent.  The  velvet 
fibers  provide  many  light  traps  and  cast  many  shadows 
which  reduce  the  relative  brightness  or  reflection- 
factor  far  below  that  of  the  flat  cardboard.  Culti- 
vated fields  on  which  there  are  growing  crops  are 
nearly  twice  as  bright  as  wooded  areas,  depending, 
of  course,  upon  the  denseness  of  the  vegetation. 
Barren  sunbaked  lands  are  generally  the  brightest 
large  areas  in  a  landscape,  the  brightness  depending 
upon  the  character  of  the  soil.  Wet  soil  is  darker 
than  dry  soil,  owing  to  the  fact  that  the  pores  are  filled 
with  water,  thus  reducing  the  reflection-factor  of  the 
small  particles  of  soil.  A  dry  white  blotting  paper  which 
reflects  75  per  cent  of  the  incident  light  will  reflect 
only  about  55  per  cent  when  wet. 

Inland  waters  which  contain  much  suspended 
matter  are  about  as  bright  as  grazing  land  and  culti- 
vated fields.  Shallow  water  partakes  somewhat  of 
the  color  and  brightness  of  the  bed,  and  deep  ocean 
water  is  somewhat  darker  than  wooded  areas.  Quiet 
stagnant  pools  or  small  lakes  are  sometimes  exceed- 
ingly dark;  in  fact,  they  appear  like  pools  of  ink,  owing 
to  the  fact  that  their  brightness  as  viewed  vertically 
is  almost  entirely  due  to  surface  reflection.  If  it  is 
due  entirely  to  reflection  at  the  surface,  the  bright- 
ness will  be  about  2  per  cent  of  the  brightness  of  the 


238  VISUAL  ILLUSIONS 

zenith  sky.  That  is,  when  viewing  such  a  body  of 
water  vertically  one  sees  an  image  of  the  zenith  sky 
reduced  in  brightness  to  about  2  per  cent. 

The  earth  patterns  were  extensively  studied  with 
the  result  that  definite  conclusions  were  formulated 
pertaining  to  the  best  patterns  to  be  used.  Although 
it  is  out  of  the  question  to  present  a  detailed  dis- 
cussion of  this  important  phase  in  this  resume,  at- 
tention will  be  called  to  the  manner  in  which  the 
earth  patterns  diminish  with  increasing  altitude.  The 
insert  in  Fig.  100  shows  the  actual  size  of  an  image 
of  a  50-foot  airplane  from  0  to  16,000  feet  below  the 
observer  as  compared  with  corresponding  images 
(to  the  same  scale)  of  objects  and  areas  on  the  earth's 
surface  10,000  feet  below  the  observer. 

For  simplicity  assume  a  camera  lens  to  have  a 
focal  length  equal  to  10  inches,  then  the  length  x 
of  the  image  of  an  object  100  feet  long  will  be  related 
to  the  altitude  h  in  this  manner: 

A  =  100  or  xh  =  1000 

iu        n 

By  substituting  the  values  of  altitude  h  in  the 
equation  the  values  of  the  length  x  of  the  image  are 
found.  The  following  values  illustrate  the  change 
in  size  pf  the  image  with  altitude : 

Altitude  h  in  feet  Size  of  image  x  in  inches 

1,000 1.00 

2,000 0.50 

3,000 0.33 

4,000 0.25 

10,000 ,.  0.10 

20,000 0.05 


CAMOUFLAGE 


239 


It  is  seen  that  the  image  diminishes  less  rapidly 
in  size  as  the  altitude  increases.  For  example,  going 
from  1000  feet  to  2000  feet  the  image  is  reduced  to 
one-half.  The  same  reduction  takes  place  in  as- 


Fig.  100.  —  Illustrating  the  study  of  pattern  for  airplanes.  The  pho- 
tograph was  taken  from  an  altitude  of  10,000  feet.  The  insert 
shows  the  relative  lengths  (verticle  scale)  of  an  airplane  of  60-foot 
spread  at  various  distances  below  the  observer. 


cending  from  10,000  to  20,000  feet.  By  taking  a 
series  of  photographs  and  knowing  the  reduction- 
factor  of  the  lens  it  is  a  simple  matter  to  study  pattern. 
An  airplane  of  known  dimensions  can  be  placed  in  the 
imagination  at  any  altitude  on  a  photograph  taken  at 
a  known  altitude  and  the  futility  of  certain  patterns 
and  the  advantages  of  others  are  at  once  evident. 


240  VISUAL  ILLUSIONS 

It  is  impracticable  to  present  colored  illustrations 
in  this  resume  and  values  expressed  in  numbers  are 
meaningless  to  most  persons,  so  a  few  general  remarks 
will  be  made  in  closing  the  discussion  of  low  visibility 
as  viewed  from  above  in  spring,  summer  and  fall. 
A  black  craft  is  of  much  lower  visibility  than  a  white 
one.  White  should  not  be  used.  The  paints  should 
be  very  dark  shades.  The  hues  are  approximately 
the  same  for  the  earth  areas  as  seen  at  the  earth's 
surface.  Inland  waters  are  a  dirty  blue-green  or 
bluish-green,  and  deep  ocean  water  is  a  greenish- 
blue  when  viewed  vertically,  or  nearly  so.  Mean 
hues  of  these  were  determined  approximately. 

Before  considering  other  aspects  of  camouflage 
it  is  well  to  consider  such  features  as  haze,  clouds 
and  sky.  There  appear  to  be  two  kinds  of  haze  which 
the  writer  will  arbitrarily  call  earth  and  high  haze, 
respectively.  The  former  consists  chiefly  of  dust  and 
smoke  and  usually  extends  to  an  altitude  of  about  one 
mile,  although  it  occasionally  extends  much  higher. 
Its  upper  limit  is  very  distinct,  as  seen  by  the  "  false  " 
horizon.  This  horizon  is  used  more  by  the  pilot  when 
flying  at  certain  altitudes  than  the  true  horizon.  At 
the  top  of  this  haze  cumulus  clouds  are  commonly 
seen  to  be  poking  out  like  nearly  submerged  icebergs. 
The  upper  haze  appears  somewhat  whiter  in  color 
and  appears  to  extend  sometimes  to  altitudes  of 
several  or  even  many  miles.  The  fact  that  the  "  earth  " 
haze  may  be  seen  to  end  usually  at  about  5000  to 
6000  feet  and  the  upper  haze  to  persist  even  beyond 
20,000  feet  has  led  the  author  to  apply  different  names 
for  convenience.  The  upper  limit  of  the  "  earth " 


CAMOUFLAGE  241 


haze  is  determined  by  the  height  of  diurnal  atmos- 
pheric convection.  Haze  aids  in  lowering  the  visi- 
bility of  airplanes  by  providing  a  luminous  Veil,  but  it 
also  operates  at  some  altitudes  to  increase  the  bright- 
ness of  the  sky,  which  is  the  background  in  this  case. 

The  sky  generally  decreases  considerably  in  bright- 
ness as  the  observer  ascends.  The  brightness  of  the 
sky  is  due  to  scattered  light,  that  is,  to  light  being 
reflected  by  particles  of  dust,  smoke,  thinly  diffused 
clouds,  etc.  By  making  a  series  of  measurements  of 
the  brightness  of  the  zenith  sky  for  various  altitudes, 
the  altitude  where  the  earth  haze  ends  is  usually 
plainly  distinguishable.  Many  observations  of  this 
character  were  accumulated.  In  some  extreme  cases 
the  sky  was  found  to  be  only  one-tenth  as  bright 
when  observed  at  high  altitudes  of  15,000  to  20,000 
feet  as  seen  from  the  earth's  surface.  This  accounts 
partly  for  the  decrease  in  the  visibility  of  an  airplane 
as  it  ascends.  At  20,000  feet  the  sky  was  found  to 
contribute  as  little  as  4  per  cent  of  the  total  light  on 
a  horizontal  plane  and  the  extreme  harshness  of  the 
lighting  is  very  noticeable  when  the  upper  sky  is 
cloudless  and  clear. 

Doubtless,  it  has  been  commonly  noted  that 
airplanes  are  generally  very  dark  objects  as  viewed 
from  below  against  the  sky.  Even  when  painted  white 
they  are  usually  much  darker  than  the  sky.  As  they 
ascend  the  sky  above  them  becomes  darker,  although 
to  the  observer  on  the  ground  the  sky  remains  con- 
stant in  brightness.  However,  in  ascending,  the 
airplane  is  leaving  below  it  more  and  more  luminous 
haze  which  acts  as  a  veil  in  aiding  to  screen  it  until, 


242  VISUAL  ILLUSIONS 

•  HI  !!•..•  •..•!..  I  |  ..— —       I.       ....-.—  -I  

when  it  reaches  a  high  altitude,  the  combination  of 
dark  sky  behind  it  and  luminous  haze  between  it 
and  the  observer  on  the  ground,  it  becomes  of  much 
lower  visibility.  Another  factor  which  contributes 
somewhat  is  its  diminishing  size  as  viewed  from  a 
fixed  position  at  the  earth.  The  minimum  perceptible 
contrast  becomes  larger  as  the  size  of  the  contrasting 
patch  diminishes. 

Inasmuch  as  there  is  not  enough  light  reflected 
upward  from  the  earth  to  illuminate  the  lower  side 
of  an  opaque  surface  sufficiently  to  make  it  as  bright 
as  the  sky  ordinarily,  excepting  at  very  high  altitudes 
for  very  clear  skies,  it  is  necessary,  in  order  to  attain 
low  visibility  for  airplanes  as  viewed  from  below,  to 
supply  some  additional  illumination  to  the  lower 
surfaces.  Computations  have  shown  that  artificial 
lighting  is  impracticable,  but  measurements  on  un- 
doped  airplane  fabrics  indicate  that  on  sunny  days 
a  sufficient  brightness  can  be  obtained  from  direct 
sunlight  diffused  by  the  fabric  to  increase  the  bright- 
ness to  the  order  of  magnitude  of  the  brightness  of  the 
sky.  On  overcast  days  an  airplane  will  nearly  always 
appear  very  much  darker  than  the  sky.  That  is,  the 
brightness  of  the  lower  sides  can  in  no  other  manner 
be  made  equal  to  that  of  the  sky.  However,  low 
visibility  can  be  obtained  on  sunny  days  which  is  an 
advantage  over  high  visibility  at  all  times,  as  is  the 
case  with  airplanes  now  in  use.  Many  observations 
and  computations  of  these  and  other  factors  have 
been  made,  so  that  it  is  possible  to  predict  results. 
Transparent  media  have  obvious  advantages,  but 
no  satisfactory  ones  are  available  at  present. 


CAMOUFLAGE  243 


Having  considered  low  visibility  of  aircraft  as 
viewed  from  above  and  from  below,  respectively,  it  is 
of  interest  to  discuss  briefly  the  possibility  of  attain- 
ing both  of  these  simultaneously  with  a  given  air- 
plane. Frankly,  it  is  not  practicable  to  do  this.  An 
airplane  to  be  of  low  visibility  against  the  earth  back- 
ground must  be  painted  or  dyed  very  dark  shades  of 
appropriate  color  and  pattern.  This  renders  it  almost 
opaque  and  it  will  be  a  very  dark  object  when  viewed 
against  the  sky.  If  the  lower  surfaces  of  the  airplane 
are  painted  as  white  as  possible  the  airplane  still  re- 
mains a  dark  object  against  the  blue  sky  and  a  very 
dark  object  against  an  overcast  sky,  except  at  high 
altitudes.  In  the  latter  cases  the  contrast  is  not  as 
great  as  already  explained.  A  practicable  method  of 
decreasing  the  visibility  of  airplanes  at  present  as  viewed 
from  below  is  to  increase  the  brightness  by  the  diffuse 
transmission  of  direct  sun-light  on  clear  days.  On 
overcast  days  clouds  and  haze  must  be  depended  upon 
to  screen  the  craft. 

In  considering  these  aspects  it  is  well  to  recall 
that  the  two  sources  of  light  are  the  sun  and  the  sky. 
Assuming  the  sun  to  contribute  80  per  cent  of  the  total 
light  which  reaches  the  upper  side  of  an  opaque  hori- 
zontal diffusing  surface  at  midday  at  the  earth  and 
assuming  the  sky  to  be  cloudless  and  uniform  in 
brightness,  then  the  brightness  of  the  horizontal 
upper  surface  will  equal  5  RB,  where  R  is  the  reflection- 
factor  of  the  surface  and  B  is  the  brightness  (different 
in  the  two  cases)  of  the  sky.  On  a  uniformly  overcast 
day  the  brightness  of  the  surface  would  be  equal  to 
RB.  Now  assuming  Re  to  be  the  mean  reflection- 


244  VISUAL  ILLUSIONS 

factor  of  the  earth,  then  the  lower  side  of  a  horizontal 
opaque  surface  suspended  in  the  air  would  receive 
light  in  proportion  to  ReB.  If  this  lower  surface  were 
a  perfect  mirror  or  a  perfectly  reflecting  and  diffusing 
surface  its  brightness  would  equal  5  ReB  on  the  sunny 
day  and  ReB  on  the  overcast  day  where  B  is  the  value 
(different  in  the  two  cases)  of  the  brightness  of  the 
uniform  sky.  The  surface  can  never  be  a  perfect 
reflector,  so  on  an  overcast  day  its  brightness  will  be 
a  fraction  (RRe)  of  the  brightness  B  of  the  uniform 
sky.  Inasmuch  as  Re  is  a  very  small  value  it  is  seen 
that  low  visibility  of  airplanes  as  viewed  from  below 
generally  cannot  be  attained  on  an  overcast  day.  It 
can  be  approached  on  a  sunny  day  and  even  realized 
by  adopting  the  expedient  already  mentioned.  Further 
computations  are  to  be  found  elsewhere.12 

Seasonable  changes  present  no  difficulties,  for  from 
a  practical  standpoint  only  summer  and  winter  need  be 
generally  considered.  If  the  earth  is  covered  with 
snow  an  airplane  covered  completely  with  white  or 
gray  paint  would  be  fairly  satisfactory  as  viewed  from 
above,  and  if  a  certain  shade  of  a  blue  tint  be  applied 
to  the  lower  surfaces,  low  visibility  as  viewed  from 
below  would  result.  The  white  paint  would  possess 
a  reflection-factor  about  equal  to  that  of  snow,  thus 
providing  low  visibility  from  above.  Inasmuch  as  the 
reflection-factor  of  snow  is  very  high,  the  white  lower 
sides  of  an  airplane  would  receive  a  great  deal  more 
light  in  winter  than  they  would  in  summer.  Obviously, 
a  blue  tint  is  necessary  for  low  visibility  against  the 
sky,  but  color  has  not  been  primarily  considered  in 
the  preceding  paragraphs  because  the  chief  difficulty 


CAMOUFLAGE  246 


in  achieving  low  visibility  from  below  lies  in  obtain- 
ing brightness  of  the  proper  order  of  magnitude. 
In  winter  the  barren  ground  would  be  approximately 
of  the  same  color  and  reflection-factor  as  in  summer, 
so  it  would  not  be  difficult  to  take  this  into  considera- 
tion. 

Seaplanes  whose  backgrounds  generally  consist 
of  water  would  be  painted  of  the  color  and  brightness 
of  water  with  perhaps  a  slight  mottling.  The  color 
would  generally  be  a  very  dark  shade,  approximating 
blue-green  in  hue. 

Aircraft  for  night  use  would  be  treated  in  the  same 
manner  as  aircraft  for  day  use,  if  the  moonlight  is  to 
be  considered  a  dominant  factor.  This  is  one  of  the 
cases  where  the  judgment  must  be  based  on  actual 
experience.  It  appears  that  the  great  enemy  of  night 
raiders  is  the  searchlight.  If  this  is  true  the  obvious 
expedient  is  to  paint  the  craft  a  dull  jet  black.  Ex- 
periments indicate  that  it  is  more  difficult  to  pick  up 
a  black  craft  than  a  gray  or  white  one  and  also  it  is 
more  difficult  to  hold  it  in  the  beam  of  the  searchlight. 
This  can  be  readily  proved  by  the  use  of  black,  gray, 
and  white  cards  in  the  beam  of  an  automobile  head- 
light. The  white  card  can  be  seen  in  the  outskirts 
of  the  beam  where  the  gray  or  black  cannot  be  seen, 
and  the  gray  can  be  picked  up  where  the  black  one  is 
invisible.  The  science  of  vision  accounts  for  this  as 
it  does  for  many  other  questions  which  arise  in  the 
consideration  of  camouflage  or  low  visibility. 

Some  attempts  have  been  made  to  apply  the  prin- 
ciple of  confusibility  to  airplanes  as  finally  developed 
for  vessels  to  circumvent  the  submarine,  but  the 


246  VISUAL  ILLUSIONS 

folly  of  this  appears  to  be  evident.  Air  battles  are 
conducted  at  terrific  speeds  and  with  skillful  maneu- 
vering. Triggers  are  pulled  without  computations 
and  the  whole  activity  is  almost  lightning-like.  To 
expect  to  confuse  an  opponent  as  to  the  course  and 
position  of  the  airplane  is  folly. 

The  camouflage  of  observation  balloons  has  not 
been  developed,  though  experiments  were  being  con- 
sidered in  this  direction  as  the  war  closed.  Inasmuch 
as  they  are  low-altitude  crafts  it  appears  that  they 
would  be  best  camouflaged  for  the  earth  as  a  back- 
ground. Their  enemies  pounce  down  upon  them 
from  the  sky  so  that  low  visibility  from  above  seems 
to  be  the  better  choice. 

In  the  foregoing  it  has  been  aimed  to  give  the 
reader  the  general  underlying  principles  of  camouflage 
and  low  visibility,  but  at  best  this  is  only  a  resume. 
In  the  following  references  will  be  found  more  ex- 
tensive discussions  of  various  phases  of  the  subject. 

REFERENCES 

1.  A  Study  of  Zollner's  Figures  and  Other  Related  Figures, 

J.  Jastrow,  Amer.  Jour,  of  Psych.  1891,  4,  p.  381. 

2.  A  Study  of  Geometrical  Illusions,  C.  H.  Judd,  Psych.  Rev. 

1899,  6,  p.  241. 

3.  Visual  Illusions  of  Depth,  H.  A.  Carr,  Psych.  Rev.  1909, 

16,  p.  219. 

4.  Irradiation  of  Light,  F.  P.  Boswell,  Psych.  Bui.  1905,  2, 

p.  200. 

5.  Retiring  and  Advancing  Colors,  M.  Luckiesh,  Amer.  Jour. 

Psych.  1918,  29,  p.  182. 

6.  The  Language  of  Color,  1918,  M.  Luckiesh. 

7.  Apparent  Form  of  the  Dome  of  the  Sky,  Ann.  d.  Physik, 

1918,  55,  p.  387;  Sci.  Abs.  1918,  No.  1147. 


CAMOUFLAGE  247 


8.  Course  on  Optics,  1738,  Robert  Smith. 

9.  Color  and  Its  Applications,  1915  and  1921;  Light  and  Shade 

and  Their  Applications,  1916,  M.  Luckiesh. 

10.  Report  of  The  Submarine  Defense  Association,  L.  T.  Bates 

and  L.  A.  Jones. 

11.  Marine  Camouflage  Design,  E.  L.  Warner,  Trans.  I.  E.  S. 

1919,  14,  p.  215. 

12.  The  Visibility  of  Airplanes,  M.  Luckiesh,  Jour.  Frank.  Inst. 

March  and  April,    1919;    also  Aerial  Photometry,  As- 
trophys.  Jour.  1919,  49,  p.  108. 

13.  Jour.  Amer.  Opt.  Soc.,  E.  Karrer,  1921. 

The  foregoing  are  only  a  few  references  indicated 
in  the  text.  Hundreds  of  references  are  available 
and  obviously  it  is  impracticable  to  include  such  a 
list.  The  most  fruitful  sources  of  references  are  the 
general  works  on  psychology.  E.  B.  Titchener's 
Experimental  Psychology  (vol.  1)  contains  an  ex- 
cellent list.  A  chapter  on  Space  in  William  James' 
Principles  of  Psychology  (vol.  II)  will  be  found  of 
interest  to  those  who  wish  to  delve  deeper  into  visual 
perception.  Other  general  references  are  Elements 
of  Physiological  Psychology  by  Ladd  and  Woodworth; 
the  works  of  Helmholtz;  a  contribution  by  Hering 
in  Hermann's  Handb.  d.  Phys.  Bk.  Ill,  part  1 ;  Physio- 
logical Psychology  by  Wundt;  E.  B.  Delabarre,  Amer. 
Jour.  Psych.  1898,  9,  p.  573;  W.  Wundt,  Tauschungen, 
p.  157  and  Philos.  Stud.  1898,  14,  p.  1;  T.  Lipps, 
Raumaesthetik  and  Zeit.  f.  Psych.  1896,  12,  39. 


INDEX 


Aberration,  19 

spherical,  122 

chromatic,  135 
Aerial  perspective,  165,  183 
After-images,  24,  25,  59,  128,  186 
,  positive  and  negative,  129 
Airplanes,  visibility  of,  233 

camouflage  for  different  types,  234 

size  of  image  at  various  altitudes, 
238 

camouflage  for  various  conditions, 

240 

Alhazen,  8 
Angles,  influence  of,  76 

various  effects  of,  81 

contours  and,  87 

apparent  effect  on  length,  91 

theories,  98 

Animals,  protective  coloration,  211 
Architecture,  195 

balance  in,    201 

Arcs,  circular,  illusions  due  to,  86 
Areas,  juxtaposed,  illusions  of,  96 
Artist,  179 
Attention,  fluctuation  of,  65,  106,  141, 

164 

Aubert,  49 

Auerbach's  indirect  vision  theory,  100 
Aureole,  178 

Balance  in  architecture,  201 

Bas-relief,  143 

Battleships,  222 

Binocular  disparity,  105 

Binocular  vision,  29,  31 

Blending  of  colors  in  camouflage,  216 

Blind  spot,  21 

Blue  light  on  war-vessels,  230 

Boswell,  varieties  of  irradiation,  122 


Brightness, 
illusions  due  to 

variations  in,  107 

and  color  contrasts,  114 

apparatus,  115 

and  hue,  125 

sky,  241 

Brucke's  theory,  37 
Brunot's  mean  distance  theory,  101 

Camouflage,  210 

terrestrial,  210 

detection  of,  215 

marine,  222 

airplane,  234 

Carr,  observations  on  distance  illu- 
sions, 108 

Chromatic  aberration,  19,  135 
Chlorophyl,  214 
Circle,  11 

arcs  of,  illusion,  86 

contracting    and    expanding    illu- 
sion, 98 
Clouds,  235 
Color,  124 

after-images,  128 

blending  in  camouflage,  216 

contrasts  and  brightness,  114 

growth  and  decay  of  sensation,  131 

illusions  of,  156 

retiring  and  advancing,  138 

saturation,  154 

sensibility  of  retina,  138 

warm  and  cold,  158 
Confusability,  226 

Confusion    theory    of    angular   illu- 
sions, 100 
Contour,  illusions  of,  52 

and  angles,  illusions,  87 


249 


250 


INDEX 


Contracting  and  expanding  circles, 

illusion  of,  98 
Contrasts,  illusions  of,  53 

simultaneous,  124,  154 

apparatus  for,  115,  125 

color,  114,  154,  188 

brightness,  114 

Convergence,  illusions  of,  108,  191 
Cord,  twisted,  illusion,  88 

Daylight,  artificial,  189 

Decoration,  painting  and,  179 

Decorator,  188 

Dember,  167 

Depth  and  distance,  illusions,  102 

Direction,  illusions  of 

Zollner's,  76 

Wundt's,  79 

Bering's,  80 
Disk,  Mason,  132 
Distance  and  depth,  illusions,  102 

and  size,  36,  104,  166 
Distance  illusions,   Carr's   observa- 
tions, 108 
Double  images,  37 
Dynamic  theory  of  angular  illusions, 


Enlargement  of   sun  and  moon  at 

horizon,  apparent,  169 
Equivocal  figures,  64 
Euclid,  8 

Extent,  interrupted,  illusions  of,  48 
External  image,  16,  17,  34 
Eye,  physiology,  13 

position,  30 

adjustments,  33 

defects,  19 

Fatigue,  128 

Field,  visual,  effect  of  location  in,  44 

Figures,  equivocal,  64 

Filters,  color,  214 

Fluctuation  of  attention,  65,  106,  141, 

164 

Focusing,  14 
Form  of  sky,  apparent,  166 


Fovea  centralis,  22,  23,  139 
Frames,  picture,  effect  of  wood  grain, 
190 

Geometrical  illusions,  44 

Glare,  119 

Grain  of  wood,  apparent  distortions 
due  to,  190 

Grecian  art,  196 

Growth  and  decay  of  colo  sensa- 
tion, 131 

Guttman,  176 

Hallucination,  4,  72 

Halo,  178 

Haze,  illusions,  etc.,  103,  166,  183 

earth  and  high,  240 
Helmholtz,  13,  74 
Bering,  74 

illusion  of  direction,  80 
Hue  and  brightness,  126 

Illusions,  geometrical,  44 

equivocal  figures,  64 

influence  of  angles,  76 

of  depth  and  distance,  102 

irradiation    and    brightness    con- 
trast, 114 

color,  124 

light  and  shadows,  144 

in  nature,  164 

in  painting  and  decoration,  179 

mirror,  205 

camouflage,  210 
Image 

after-,  24,  25,  59,  128,  129,  186 

double,  37 

external,  15,  17,  34 

retinal,  inversion  of,  16 

of  airplane,   size  at  various  alti- 
tudes, 238 
Indirect  vision  theory,   Auerbach's, 

100 

Intaglio,  143 

Interrupted  extent,  illusions  of,  48 
Iris,  16 
Irradiation,  120 


INDEX 


251 


and  brightness  contrast,  114 
varieties  of  (Boswell),  122 
in  architecture,  199 

James,  170 
Jastrow,  80 
Jones,  L.  A.,  223 
Judd,  86,  93 
Judgment,  1 

Karrer,  160 
Kepler,  8 

Light,  effect  of  spectral  character,  189 

Lighting,  illusions  of  depth  and  dis- 
tance due  to,  102 
contrasts,  154 
diffusion,  effect  of,  145 
direction,  effect  of,  144,  151 
ending  of  searchlight  beam,  160 
warm  and  cold  colors,  158 

Lipps,  10,  11 

dynamic  theory  of,  99 

Location  in  visual  field,  effect,  44 

Mean  distance  theory,  Brunot's,  101 
Mechanical,  esthetic  unity,  11 
Magician,  3 
Magic,  mirror,  205 
Marine  camouflage,  222 
Mason  disk,  132 
Mirage,  3,  176 
Mirror  magic,  205 
Miscellaneous  color  effects,  140 
Moon,  apparent  size  at  horizon,  8 
36,  169 

theories  of,  173 

apparent  radius  of  crescent,  121 
Miiller-Lyer  illusion,  53,  93 

National  Research  Council,  Commit- 
tee on  Camouflage,  234 
Nature,  164 
Necker,  74 

Qppel,  9 


Painting  and  decoration,  179 
Painter,  2,  179,  186 
Parallax,  105 
Parthenon  of  Athens,  196 
Persistence  of  vision,  131 
Perspective,  68 

in  architecture,  198 

aerial  166,  183 

theory,  98 
Photographer,  152 
Photography,    use    in    detection    of 

camouflage,  220 
Photometer,  166,  217 
Pigments,  184 
Poggendorff  illusion,  86 
Protective  coloration,  animals,  211 
Psychology,  2,  6,  157 

of  light,  193 
PurMnje  phenomenon,  26,  139 

Reflection-factors,  236 
Retina,  14,  20 

inertia,  130 

color  sensibility,  138 
Retinal  rivalry,  140 
Retiring  and  advancing  colors,  136 
Reversal  of  mirror  image,  205 
Rods  and  cones,  21 

Schroder's  staircase,  70 
Sculpture,  204 

Searchlight  beam,  ending  of,  160 
Sensation,  color,  growth  and  decay, 

131 

Sense,  1 

Shading,  counter,  for  vessels,  224 
Shadows,  importance  in  camouflage, 

215 
Size  and  distance,  35,  36 

illusions  of,  104,  166 
Sky 

apparent  form  of,  166 

brightness,  241 

Skylight  and  sunlight,  relative  pro- 
portions of,  216,  243 
Smith,  Robert,  173 
Smoke-screens,  230 


252 


INDEX 


Spectral  character  of  light,  189 

Sphere,  illusions,  145,  150,  151 

Spherical  aberration,  19 

Sphinx  illusion,  206 

Spiral  illusions,  90 

Spraying,  paint,  187 

Stereoscope,  39,  142 

Stereoscopic  vision,  38,  41,  141 

Submarines,  225 
camouflage  for,  232 

Sun,  apparent  enlargement  at  hori- 
zon, 169 

Sunlight  and  skylight,  relative  pro- 
portions in  nature,  215,  243 

Terrestrial  camouflage,  210 
Theory  of  influence  of  angles,  98 

perspective,  98 

dynamic,  99 

confusion,  100 

indirect  vision,  100 

mean  distance,  101 
Thiery's  figure,  71 
Thiery's  perspective  theory,  99 


Transparencies,  185 
Twisted  cord  illusions,  88 

Uibe,  167 

Vertical  vs.  horizontal  distances,  11, 

36,  46 
Visibility,  low,  for  vessels,  222 

of  airplanes,  233 
Vision,  29 

persistence  of,  131 

stereoscopic,  38 
Visual  perception,  32,  33 

Warm  and  cold  colors,  158 
Warner,  E.  L.,  227 
Wheatstone,  37 

Wood  grain,  illusions  caused  by,  191 
World  War,  213 
Wundt,  10,  11,  32,  74 
illusion  of  direction,  79 

Yellow  spot,  139 

Zollner's  illusion,  67,  76 
Zoth,  176 


OTHER    BOOKS 
BY 

M.  LUCKIESH 


COLOR  AND  ITS  APPLICATIONS 

Second  Edition,  Revised  and  Enlarged. 

6x9, 150  illustrations,  4  color  pktes,  431  pages .  $4.50 

The  object  of  this  treatise  is  not  only  to  discuss  the 
many  applications  of  color,  but  to  establish  a  sound  scientific 
basis  for  these  applications.  The  book  is  authoritative, 
well  illustrated,  and  contains  many  references  and  a  wealth 
of  new  material.  It  was  written  by  an  investigator  in  the 
general  field  of  color  and  is  therefore  not  narrowly  limited 
in  scope.  It  fills  a  distinct  gap  that  has  existed  on  the 
book  shelves. 

LIGHT  AND   SHADE   AND    THEIR   APPLICA- 
TIONS 

6x9, 135  illustrations,  277  pages $3.00 

The  book  is  a  condensed  record  of  several  years'  research 
by  the  author  in  the  science  of  light  and  shade.  It  is  the 
first  published  work  which  deals  with  the  science  of  light 
and  shade  in  a  complete  and  analytical  manner.  The  author 
has  the  faculty  of  bringing  forth  scientific  facts  in  such  a 
manner  as  to  be  helpful  to  those  interested  in  the  various 
arts.  The  book  is  of  extremely  wide  interest  because  it 
deals  with  the  appearances  of  objects  and  hence  with  vision 
and  with  lighting.  It  is  well  illustrated  and  represents  the 
first  elaborate  attempt  to  formulate  the  science  of  light  and 
shade  and  to  correlate  it  with  various  arts. 

ULTRAVIOLET    RADIATION,    Its    Properties, 
Production,  Measurement  and  Applications. 

6  x  9,  12  plates,  270  pages $3.50 

It  is  the  primary  aim  of  this  book  to  present  authentic 
data  of  such  scope  as  to  be  useful  to  the  chemist,  physicist, 
engineer,  biologist,  ophthalmologist  and  physician  and  others 
interested  in  ultraviolet  radiation.  Theory  has  been  sub- 
ordinated to  experimental  facts  because  the  latter  are  not 
affected  by  the  inevitable  changes  in  theory.  Much  of  the 
literature  on  this  subject  is  confusing  because  of  the  lack 
of  care  in  the  choice  of  definitions  and  of  limited  value 
resulting  from  carelessness  in  specifying  important  factors. 
From  this  mass  of  isolated  material  the  author  has  coor- 
dinated much  valuable  data.  The  many  references  which 
are  included  increase  the  usefulness  of  the  book. 


LIGHTING  THE  HOME 

5  x  7J,  illustrated,  289  pages $2.00 

This  is  a  pioneer  book.  It  ranks  with  books  on  interior 
decoration  and  furniture  as  a  help  toward  transforming  a 
house  into  a  home.  It  is  practical  hi  that  it  offers  advice 
on  all  sorts  of  lighting  problems  and  it  is  fascinating  reading 
as  well. 

ARTIFICIAL  LIGHT,  ITS  INFLUENCE  ON 
CIVILIZATION 

6x9,  illustrated,  366  pages $3.00 

This  story  of  the  achievements  of  artificial  light  is  written 
especially  for  the  man  in  the  street  who  is  not  interested 
in  technical  scientific  terms  and  formulae,  but  who  looks 
with  admiration  upon  the  huge  signs  which  flash  and 
sparkle  above  the  crowds  on  the  Great  White  Way,  who 
marvels  at  the  colors  and  brilliance  of  a  spectacular  theatri- 
cal production  and  desires  to  know  how  it  is  accomplished, 
and  who  takes  a  natural  delight  in  hearing  about  scientific 
discoveries  when  they  are  explained  hi  the  simple,  vivid 
language  he  understands  best. 

THE    LIGHTING    ART,    ITS    PRACTICE   AND 
POSSIBILITIES 

6x9,  illustrated,  229  pages $2.50 

This  book  discusses  lighting  as  engineering  plus  art,  and 
treats  the  subject  as  a  branch  of  interior  and  exterior 
decoration.  The  technical  aspect  of  the  subject  is  not 
neglected,  but  the  main  emphasis  is  upon  the  "  why  "  and 
not  merely  the  "  how  "  of  lighting. 

THE  LANGUAGE  OF  COLOR 

6x9,  illustrated,  282  pages $2.00 

A  practical  volume  on  color,  the  various  fields  in  which 
it  is  used  and  its  importance  in  portraying  the  ideas  that 
make  for  progress.  A  book  of  special  interest  to  all  those 
who  deal  hi  color  schemes  and  values. 

THE  BOOK  OF  THE  SKY 

6x9,  illustrated,  236  pages $3.50 

"  The  beauties,  wonders,  awesome  spectacles,  inspiring 
panoramas,  and  extensive  ranges  of  vision  which  await 
the  aerial  traveler,  make  of  cloudland  a  veritable  fairyland 
if  he  will  open  his  consciousness  to  them.  Aircraft  have 
brought  this  new  world  of  experiences  within  easy  reach 
of  mankind  and  it  is  one  of  the  aims  of  this  volume  to 
awaken  those  who  fly,  or  would  fly,  to  the  variety  of 
interest  which  ah*  travel  affords." 


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